Distributed computing (DC) system is widely implemented due to its low setup cost and high computational capability. However, it might be vulnerable to malicious attacks like computer virus due to its network structure. The service reliability, defined as the probability of fulfilling a task before a specified time, is an important metric of the quality of DC system. This paper attempts to model and compute the service reliability for the DC system under virus epidemics. Firstly, the DC system architecture is modeled by an undirected graph whose nodes (i.e. computers) have a continuous-state model representing its computational capability. Then a set of epidemic differential equations are formulated and solved to obtain the state dynamics of each node under the virus epidemics. A universal generating function (UGF) based approach is proposed to calculate the service reliability of DC system. Numerical results show the effectiveness of the proposed method. The sensitivity analysis on the model parameters, the comparison with centralized computing system and the optimization of defense level parameter are also conducted.