We consider an M$_1$, M$_2$/G/1/ K retrial queueing system with a finite priority queue for type I calls and infinite retrial group for type II calls where blocked type I calls may join the retrial group. These models, for example, can be applied to cellular mobile communication system where handoff calls have higher priority than originating calls. In this paper we apply the supplementary variable method where supplementary variable is the elapsed service time of the call in service. We find the joint generating function of the numbers of calls in the priority queue and the retrial group in closed form and give some performance measures of the system.