The present invention relates to a method of controlling common call connection and a media gateway for executing the method, which are capable of performing call connection control without a change in a control procedure under different protocols and the interworking of the different protocols. In the method of the present invention, each of a plurality of termination points connected by a call in the media gateway, each of a plurality of multimedia services transmitted and received between the terminations through connection setup of the call and each of a plurality of physical resources per multimedia service in the multimedia are defined as a termination, a stream and a channel, respectively, a call processing request based on one of various media gateway control protocols is mapped into a model defined as described above, and resource allocation, connection setup or release with respect to a channel belonging to a call and a termination are requested according to the type of the call processing request. Accordingly, the method of the present invention accommodates call processing based on various types of protocols.