It sounds like either the seat (what the flapper closes on) of the
flush valve is worn or you may have a small leak in the flush valve
gasket. They have a kit at the Home centers to glue a new seat on top
of the old one (make sure it is very dry before you install or just
replace the entire flush valve assembly (including the gasket on the
flush valve), kit for this is also available. Don't over tighten the
gasket as it will then warp in short time and you will be right back to
where you started.

Either bring with you pictures and measurements or bring in old part to
insure you get the right kit the first time.