Priority mechanism is an invaluable scheduling method that allows customers to receive different quality of a service. Service priority is clearly today a main feature of the operation of any manufacturing system. We are interested in an M1,M2/G1,G2/1 priority retrial queue with pre-emptive resume policy. For the model in question, we discuss the problem of ergodicity, and by using the method of supplementary variables, we find the partial generating functions of the steady state system state distribution. Moreover, some pertinent performance measures are obtained and numerical study is also performed.