Abstract: Laying power cables along the bridge is a new way of laying submarine cables across the sea. This paper focuses on the vibration of power cables laid on sea-crossing bridges induced by automobile and vehicle traffic loads. The overall combined structural analysis model of the bridge and cable is established, and the automobile and vehicle loads are simplified into random moving concentrated load sequence. The pseudo-excitation method (PEM) is developed to calculate the standard deviation and evolutionary power spectrum density of displacement and stress responses of the cable under random moving loads. The influence of automobile and vehicle speed on the standard deviation of cable dynamic response is studied. The PEM transforms the problem of random moving loads into dynamic response analysis under simple harmonic moving loads with specific frequencies, and it can calculate the standard deviation of dynamic response of the cable which is very consistent with Monte Carlo (MC) method, but the number of time-domain response analysis required is far less than that of MC method. The numerical results show that the standard deviation of displacement and stress of the cable increases with the increase of automobile and vehicle running speed. Under automobile and vehicle traffic loads, the standard deviation and power spectrum of displacement of aluminum sheath are larger than that of the cable core, which may make the fatigue failure of the cable occur in the aluminum sheath layer first. This work has a certain reference significance for the actual project of cable laying along the sea-crossing bridges.