If you want to keep most of your iPhone call history, yet only want to delete individual call records all you have to do is tap on Setting on the Home screen of your iPhone. From that point, tap on the Recents tab that you’ll find at the bottom of the screen, then tap on Edit in the upper right hand corner.

After you have tapped on Edit on your iPhone when you want to delete individual iPhone calls, just tap on the delete option next to the call you want to remove from your history. You will then be able to confirm that you want it deleted.