You should probably use framerate-independent movement, because then you wouldn't have to care about the FPS.
What you are probably doing right now is in every frame you say
position += velocity;, where
position is in units of distance (whatever they may be--pixels, meters, etc.), and
velocity is in units of distance per frame.
However, what you should probably do is have
velocity instead be in units of distance per time instead of distance per time. Then what you would do is
position += velocity * frameTime;, where
1/FPS, and is in units of time (seconds, to be specific).
Now, no matter what the framerate is, your character will move the same distance in the same amount of time.