SIP is a flexible and extensible call setup protocol that may be combined with other protocols used in the Internet to make various services like voice communication. Voice communication can be classified into normal calls used for communication between common users and emergency calls for 112, 119 and other services through public safety networks. It is required to research to process effectively these normal calls and emergency calls through public networks such as the Internet. In this paper, we propose a bypass scheme for emergency calls by giving priority to INVITE messages for them and processing them with priority in the SIP proxy queue. We perform simulation studies using the network simulator ns-2 for the performance evaluation. Simulation results show that the proposed scheme processes emergency calls faster than normal calls and thus it is expected to make a special purpose network like the national disaster network efficiently by using the existing Internet.