The condition monitoring and faults diagnosis of wheelset are of great significance for the safe and stable operation of trains. Aiming at the axle crack, wheel flat, wheel out-of-roundness and their coupling faults in wheelset system, this paper proposes a method to diagnose these multiple faults simultaneously. Firstly, the dynamic model of a wheelset system with flat and out-of-roundness is established in SIMPACK software to analyze the fault characteristics of these two typical wheel damages. And the wheel flat and out-of-roundness are equivalent to displacement excitation and then loaded into the finite element (FE) model of the cracked wheelset. The vibration responses of the cracked wheelset with flat and out-of-roundness are solved in ABAQUS software. Then, the simulated multi-fault vibration data of wheelset are input into a Light-GBM model to realize the faults classification of axle crack, wheel flat, wheel out-of-roundness and their coupling faults. Finally, the wheelset vibration signals under the conditions of health, axle crack, wheel flat, and crack-flat coupling fault are collected from an experimental bench to verify the proposed method. This work can provide a basis for multi-fault classification and on-line health monitoring of trains.