Box-booms are widely used in some cranes. The strength of box-booms would continuously deteriorate with the use of time. In this paper, gamma process is employed to describe strength degradation when dealing with the overall stability of the box-boom. Furthermore, the total working time is not deterministic but random because of the random arrivals of tasks and the random working time of every task. By accounting for strength degradation and the random total working time, a time-dependent reliability-based design optimization(RBDO) model for the box-boom is proposed. An engineering case is used to illustrate the proposed model.