Maritime transportation has kept a steadily fast development in recent decades, which puts higher requirement to the port operation. Lots of works addressed the integrated scheduling of berth and quay crane, however, most of them ignore the impact of maintenance activities, especially, the uncertain quay crane maintenance. In this paper, we investigate an integrated berth allocation and quay crane assignment with uncertain quay crane maintenance activities, and establish a stochastic integer linear programming model to minimize the excepted total turnaround time of vessels. A sample average approximation method is applied to solve the problem. Numerical experiments with 90 instances are conducted, which verify the accuracy and efficiency of the proposed model and method.