The paper deals with a single server queue with two priority classes of customers. The arrival process for the high-priority class is assumed to be Poisson, while the interarrival time for the low-priority class is allowed to have a general distribution. Work-conserving rules, especially the non-preemptive rule and the preemptive-resume rule, are studied. A relationship between the unfinished work and the waiting times for both priority classes is derived. Numerical calculation for the unfinished work is not so easy, because the queueing model considered here contains the GI/G/1 model. Using a diffusion approximation for the unfinished work process, new approximate formulas for the performance measures are obtained explicitly. If the arrival process for the low-priority class is also Poisson, the formulas are consistent with the classical exact results. Numerical examples and comparisons with simulation results are presented. They indicate that the approximate formulas proposed here are accurate as compared with those presented in the previous works.