Many of multimedia applications in distributed systems should transmit continuous audio/video across networks when clients request. Typically, messages for continuous media in packet-switched networks are split into periodic, different sized packets with deadlines. Since clients request different typed services, traffic streams are heterogeneous. Furthermore, since the continuity of continuous media should be preserved, non-preemptive scheduling is preferred in multimedia communications. In this paper, we present a new non-preemptive scheduling algorithm which guarantees the timely delivery of more sets of messages for continuous media on a communication link connected to packet-switched networks. It schedules messages by using a heuristic based on the earliest deadline first (EDF) policy. It can always find a feasible schedule for messages which are schedulable by the EDF algorithm. We also present admission control given as sufficient conditions for a set of messages to be schedulable by the our scheduling algorithm for controlling the traffic load on a link. If a new request and the previous messages satisfy these conditions, it accepts the new request. The accepted message transmission is done like the circuit-switched transmission non-preemptively. Finally, we show the improvements in performance of our scheduling algorithm by simulation results.