The remaining useful life (RUL) prediction of degradation equipment is a hot topic in the field of reliability research. Based on the Wiener process, a RUL prediction method considering random shocks is proposed here. Firstly, the continuous degradation process of the equipment is described by a nonlinear Wiener process, while the random shocks leading to the mutation of the degradation level is characterized by a compound Poisson process. Secondly, based on the established stochastic degradation model and the concept of the first hitting time, the approximate analytic probability density function of RUL are deduced, which greatly reduces the numerical computation time, and a model parameter estimation method based on the expected maximization algorithm is proposed. Numerical simulation and the aerospace lithium battery example indicate that, the proposed method improves the accuracy of RUL prediction, and it has certain theoretical guiding significance for solving the RUL prediction problem of equipment with random shocks.