Abstract: The vibration of maglev vehicle-bridge coupled system induced by random guideway irregularities is one of the major concerns for running maglev trains. Traditional methods for random vibration analysis are tedious and time-consuming. The explicit expressions for the dynamic responses of the maglev vehicle and the bridge subsystems with respect to the interacting electromagnetic force were first formulated. By applying the electromagnetic force formula and the displacement compatibility condition between the vehicle and the guideway, the explicit expression for the electromagnetic force in terms of guideway irregularities was further derived. Subsequently, the explicit expressions for the critical responses of the maglev vehicle and the bridge subsystems subjected to guideway irregularities were elicited. Based on the explicit formulations, the evolutionary statistical moments of critical responses of the maglev vehicle and the bridge subsystems were calculated by direct application of the statistical moment operation rules. In addition, a random simulation method was put forward to obtain the statistical metrics of critical responses of the maglev vehicle-bridge coupled system with generated guideway irregularity samples. Owing to the merits of explicit formulations, a more efficient stochastic analysis of the maglev vehicle-bridge coupled system was achieved. A coupled model involving a 2-DOF maglev vehicle and a simply-supported beam was used to demonstrate the formulation procedure of the proposed method. The numerical example with a maglev train traversing a multi-span bridge indicates that the explicit time-domain method has high accuracy and superior computational efficiency.