In this paper, we study the performance of service systems with priority upgrades. We model the service system as a single-server two-class priority queue, with queue 1 as the normal queue and queue 2 as the priority queue. The queueing model of interest has various applications in healthcare service, perishable inventory and project management. We give a comprehensive study on the system stationary distribution, computational algorithm design and sensitivity analysis. We observe that when queue 2 is large, the conditional distribution of queue 1 approximates a Poisson distribution. The tail probability of queue 2 decays geometrically, while the tail probability of queue 1 decays much faster than queue 2's. This helps us to design an algorithm to compute the stationary distribution. Finally, by using the algorithm, we do sensitivity analysis on various system parameters, i.e., the arrival rates, service rates and the upgrading rate. The numerical study provides helpful insights on designing such service systems.