I have a city or normal bike and I want to ask, that with the necessary modification except the frame, is possible to convert this bike in a road bike?
Depends what you mean by city bike and road bike.
If you mean converting a bike with flat bars to one with drop bars there are issues. Flat bar bike frames are typically longer than drop bar frames, because flat bars place the rider's hands closer to the head-tube than drop bar hoods or drops hand positions do. Also, compatibility of brakes, levers/shifters and derailleurs can be problematic.
It is very likely you would end up replacing a significant fraction of the components on the bike, and it would be more cost effective to sell it and buy the bike you want.