There is a deviation between finished bridge and design requirement of prestressed concrete (PC) cable-stayed bridge due to the construction errors in construction process. Besides, the randomness of construction errors will cause the variability of structure system in construction state. However, the most common analyses considering construction errors are based on deterministic analysis method, which concern the mean errors effect merely. These are inadequate obviously. In this paper the main construction errors of PC cable-stayed bridge and corresponding distributions are outlined firstly. Also several common stochastic analysis methods are introduced. Using Monte-Carlo method with ANSYS finite element analysis (FEA) software, then, a stochastic analysis of a single tower PC cable-stayed bridge considering construction errors is completed, and the probability characteristics of structural response under dead load are obtained. Finally, from the reliability point of view, the influence of randomness of construction errors on structural safety and the necessity of stochastic analysis for PC cable-stayed bridges are discussed.