You don't say what type ie: Float ball and arm or the more modern one like upside down cup running up a ratched type rod as water level rises so does the float eventually shutting water off.
You also don't say if this is a new fault or it's been slow filling from new.
Have you had the water turned off for any reason? as it may be the water pressure needs to be lifted by opening the stop valve more, tank or main fed.
More details would be helpful.
Bob
August 2009