I recently got a canon 550D with a battery grip (BG-E8) and I love it, but as the grip is heavy I want to use the body only,but when I apart the grip and put the battery inside the camera, it would not turn on... when I get the camera It had only a grip, no cover for the battery, I think its a problem, the camera wont turn on without a cover... This may be a stupid question but I am a begginer and any answer will help.
yes the camera will not turn on without the battery cover in place. However, the battery cover is fully detachable and has to be removed completely for the battery grip to be fitted. It is also likely to be a very cheap replacement part.
Before you go looking for a replacement one though, take a look on the battery grip itself. See in this picture: The part of the grip that fits into the battery compartment of the camera has a holder for the normal battery cover.
If it is in place, or if you get a replacement cover, to fit it to the camera, you normally push it fairly gently into the hinge at approximately a 45 degree angle (ie approximately half way to perpendicular when opened).
As an aside, you didn't mention in your question, but in case you're using two Canon batteries in the battery grip, you can save a little bit of weight because I think it will work with just one battery in the battery grip
There is a slot in the grip to store the battery door. Look at the lower end of the part of the grip that is inserted into the battery well of the camera. If the battery door is not stored there, you need to contact the place from which you bought the camera and find out what they did with it.