My toilet closet seems to be leaking water in the toilet bowl.The causes the water system to keep pumping water into the closet to maintain the water level. What can I do to solve the problem

If you losing water from in the tank into the toilet bowl, you need a tank valvel seal. Most toilets have a flapper ball type seal that connects to your flush handle. If your toilet has this type set up it's as easy as removing the old flapper ball from two plastic hooks and slipping a new on. 2 or 3 minutes at max.

I use Korky brand replacement balls and here's a link to identify it for you.

Korky Brand Toilet Tank Repair Products

Thanks a lot malex27, I sure hope it stops leaking after I change the flapper, I am irritated by the refilling of the tank every time the water level drops. But I have only just changed that flapper, about 6 months ago, do I have to keep changing flappers every now and then?

No a flapper should last much longer than 6 months to answer your question sammie. I'm sure the amount of minerals in your water could affect the life of the gasket, but if it's only 6 months old I would start by lifting the flapper up and feeling for any sediment or other debri that would be preventing it from sealing. Some times debri works it's way under the seal and simply needs to be cleaned off.

Just wondering, after you replaced the flapper last time, did it stop your leak until now? Also how often does the tank refill?

Yes, it stopped leaking and there does not seem to be any debris on its surface when I checked. It refills almost every 30-50mins.

Sounds like your flapper linkage needs adjusting.
With the flapper seated the linkage wants to have 1/4" of play. Too much play and the flapper doesn't get pulled back enough giving you a short flush. Too tight and it lets water seep past the flapper. I adjust the chain by the link and if it needs fine tuning, I bend the flush lever rod a bit untill I have the desired play in the linkage. One more thing about a flapper. you will see where the old flapper hooks onto the base of the white overflow tube. On a older type with no hooks the flapper has a ring that slips down over the overflow tube to the seat. If your tank has hooks, take a sharp knife or scissors and cut the neoprene ring off on the marks provided and hook the flapper on the hooks. Leaving the ring on will interfere with the flush. The water level in your tank should be 3/8 to 1/2" below the top of the overflow tube when the tank's filled. Good luck, Tom