Take the top off your tank and then flush and watch what happens. There is usually a black rubber flap at the bottom of the tank. That rubber flap comes up when the toilet is flushed then goes down to seal the tank so that it can refill. It may not be sealing correctly so you are actually running new water into the tank after the flush is finished.
The other thing that could be wrong is that the float (the big ball at the end of the arm) may not be set correctly. When the toilet is flushed the float drops, as the toilet refills the water will cause the float to rise and then hits a point where the water shuts off. There is a screw at the end of the arm opposite the float that you can adjust with a screwdriver if you think the float is your problem. Adjust the screw and flush; then readjust and flush again until you get it set right.
Don't fret if you find a problem - replacing the "guts" in the tank is an easy job if you can read directions and use basic tools (don't forget to turn off the water to the toilet if you need to replace the guts). Good luck! Judy