Can I go for H1 visa when I already have B1 visa approved.

My employer file for B1 visa and it got approved. Now they want to file for H1 visa too. Wanted to know if I am allowed to file for H1 when I already have B1 visa however never traveled to US on B1.

You can appear for it as long as you are qualified for the same. There is a possibility that they may cancel B-1 visa stamp w/o prejudice when approving H-1, which is normal.