Backlog Grooming in the middle of the Sprint? Doesn't that break the "Focus" value ?"

Since it's not an event, the Scrum Guide doesn't define how or when refinement occurs. This is up to the discretion of each team.

Most of the teams that I've worked with do have refinement spread throughout the Sprint, but they do it in different ways. Some teams meet and do refinement as a group. Others meet briefly, identify Product Backlog Items near the top of the backlog that they don't think are ready, and people pick the ones they'll invest some time refining as individuals or small groups. In my experience, a team will need plenty of time to think and understand the work, and work will often need to be talked about multiple times before the team considers it to be ready for selection in an upcoming Sprint.

At the end of the day, do what works for your team. If you're having specific problems, such as planning a Sprint or being able to execute on your Sprint Goal commitment or if people on the team find refinement to be difficult, then you can focus on those specific problems. There are certain problems where I would look at the team's refinement practices to understand potential solutions. But without understanding problems faced by the team, I wouldn't feel comfortable suggesting that the team change their refinement practices.

Often I see a team's focus impacted by unplanned surprises where someone wants the Product Owner to add some work to the Sprint, distractions, not focusing on a Sprint Goal, high work in progress, multi-tasking, etc. If someone was reading their email or texting during a refinement meeting, that could impact focus. I feel those examples align with the spirit of the Scrum Value of focus.

I believe its not convenient for our team to gather around and do backlog grooming in the middle of an active Sprint. 

That's fine - how does the rest of the team feel?

Thomas gave some great tips. Refinement could even be done ongoing by one person, or it could even be done in Sprint Planning. But in my experience without some refinement activities Sprint Planning won't be as effective.

FYI - We don't use the term 'grooming' anymore. It was removed from the Scrum Guide over 12 years ago and replaced with 'refinement'.

If you don't work on refinement of the Product Backlog during a Sprint, when would you do it?  Are you advocating for having the Developers pull items from the Product Backlog into a Spring Backlog before they have refined them to a point to determine if they can be completed during a single Sprint?

Backlog refinement is not an event.  It is an on going activity that is undertaken by the Scrum Team.  I have worked with many teams that did a large part of their refinement individually.  They would use whatever system used to capture the Product Backlog (for example Jira) and make comments in the items that everyone could see.  They would asynchronously discuss the item and arrive at some decisions.  Not everything required them to meet in person, though some in person discussions did occur based upon the individual findings. 

I have never been involved with a team that used your process but I could see how it would be beneficial. As both @Thomas and @Chris stated, it is up to individual teams to decide what works best for them.  As a Scrum Master, I encourage them to do that and to re-evaluate their decisions from time to time. 

FYI - I'm going to add to @Chris' statement about grooming.  In some cultures the term "grooming" has some very negative implications.  While I understand that most people use it to mean a mechanism for "making things better" such as animal grooming, for some people it is not accepted well. Refinement is a better term as it more accurately reflects the activity that is being undertaken. 

we do backlog grooming after the sprint retrospective . And before the nex sprint planning

That means you're doing it after the Sprint ended, right at the beginning of the next Sprint just before Sprint Planning. In Scrum the Sprint Retrospective is the last thing to happen, and there are no gaps between Sprints.

I believe its not convenient for our team to gather around and do backlog grooming in the middle of an active Sprint. And scatter their focus on preparing for the next sprint while we still have work on hands in the current sprint . 

Product Backlog refinement is the art and science of making work ready for Sprint Planning. Is it really "convenient" to defer the risk of work not being ready so late?

Bear in mind that the critical output of the Sprint Review is an updated Product Backlog. It's the last responsible moment to get the Product Backlog in order before the next Sprint begins. You've only got the Sprint Retrospective to go, and then you'll be straight into it.  If that isn't happening, what are you doing in a Sprint Review?