if all stars look like they are still but are actually moving at a very high speed then why is our sun not moving............???

Stars does not move. To a person viewing the stars from the earth, they seem to move because the earth rotates. Hence, the Sun does not move too.

------Hope this answer helped.

 ALL STARS MOVE AROUND THIER GALAXY . BUT IF WE SAY WITH RESPECT TO EARTH , THEY DO NOT MOVE . SUN WITH THE WHOLE OF THE SOLAR SYSTEM ROTATES AROUND MILKY WAY IN THE ORION ARM AND EVEN TOWARDS THE CENTRE . WE ARE COMPLETING ONE ROATATION AROUND MILKY WAY THIS YEAR 2012 .

sun is too a star and as usual the laws of physics do apply on all. the equator of the surface of the sun rotates every in 25.4 days. in front of sun the earth is very small .its magnetosphere is very strong &earth is also moving so we cannot see it moving.