This paper considers an M/M/1 queue that handles arrivals form 2 classes of customers on a preemptive priority basis,  where the lower-priority customers with finite buffering.  The queue model can be described in a quasi-birth-and-death (QBD) process with finitely many phases. By matrix-geometric method,  we get the formula of stationary queue length distribution,  and illustrate the effectiveness of the method by numerical examples.