We describe a new parallel algorithm for discreteevent simulation on exclusive-read exclusive-write parallel random-access machine (EREW PRAM). This algorithm is based on a recently developed parallel data structure, namely parallel heap, which when used as a parallel event-queue, allows deletion of O ( p ) earliest messages and insertion of O ( p ) new messages each in O(1og n ) time, using p processors, where n is the number of messages scheduled. Our algorithm can simulate up to p independent messages in O(1og n ) timethus achieving O ( p ) speedup. The number of processors, p , can be optimally varied in the range 1 5 p 5 n . To our knowledge, such a theoretical efficiency in a parallel simulat.ion a l g o r i h i has been achieved for the first time.