A system and a method for controlling transport rate of real time streaming service between a streaming server and a streaming client connected via a predetermined network. In transmitting multimedia contents to the streaming client, the streaming server controls the transport rate by compensating as much as accumulatively added average value a difference between a buffer level reported from the streaming client and a required buffer level. Furthermore, in order to prevent an initial reproduction delay, the streaming server controls by a maximum transport rate allowed by the network. By which, an overflow or an under-run of buffer occurring when streaming service is given for a long time can be prevented, and a time delay can be minimized from a time of streaming start point to a time of reproduction in actual screen or sound.