Doing scrum with Kanban board

Scrum.org has a wide range of material about Kanban within the context of a Scrum team. They have a set of suggested readings for the Professional Scrum with Kanban certificate, which will be relevant even if you aren't going after the certificate. Other people and organizations have also written about combining Scrum and Kanban (sometimes referred to as Scrumban). It's not an uncommon combination.

Indeed, not uncommon and a very strong combination in some circumstances

I have 2 teams doing exactly that right now.  Look at the material that @Thomas suggested.  Kanban within Scrum framework is possible and for some teams works better. 

Is it possible to work with Scrum, I mean all events, artifacts, etc but work on Kanban board?

Yes, although it might be more useful to think of Kanban as a strategy.

Thank you for the replies, but will the framework still be called Pure Scrum or Scrum or it will not be Scrum any more and will be called Scrumban? In this case what kind of board does Scrum use? Scrum Board?

If you don't change Scrum (keep doing it as defined), then it is still Scrum.  Just like when you add XP practices or TDD practices or any other practice on to the Scrum Framework, it is still Scrum.  Scrum is a framework from which process evolves.  You add the right practices for you to be successful.  Scrum is simple and can be added to.  Scrum with XP is still Scrum for example.  Adding Kanban practices to Scrum is still Scrum. Now if you for example stop doing Retrospectives (I am just using it as an example) then you are no longer doing Scrum.

Hi Anahit, like others here mentioned, many Scrum teams use Kanban as a strategy to improve flow, which includes visualizing their work and workflow by using a Kanban Board as well as limiting their WIP, actively managing the work in flight, and inspecting and adapting the workflow and applying empiricism to how the workflow is defined. 

The Kanban Guide for Scrum Teams mentioned above is a great reference for this approach and like Eric said it's still Scrum. It's Scrum using Kanban as a complementary practice/strategy for improving flow and therefore improving empiricism.