［Purposes］ The paper aims to explore the stress state and calculation method of unbalanced moment of multi-point support swivel system under unbalanced moment condition, so as to ensure stress safety of the swivel structure and provide basis for balancing counterweight before swivel. ［Methods］ The local finite element analysis model of asymmetric cable-stayed bridge was established by the finite element software of ABAQUS, the stress of the ball joint and turntable under the condition of five-stage unbalanced moment was compared and analyzed. By quantifying the influence of stress concentration on the prediction accuracy of unbalanced moment, the traditional calculation formula of unbalanced moment was improved. ［Findings］ The stress at the edge of the ball joint is much higher than that at the inside. The increase of unbalanced moment will cause reverse change of contact stress on both sides of the ball joint. Multi-point support can reduce the peak stress of the ball joint and turntable. The predicted value of the improved formula is in good agreement with the simulating input value. ［Conclusions］ The simulation results show the safety of the swivel structure under unbalanced moment condition. At the same time, the improved unbalanced moment prediction model is convenient to calculate, can reduce the traditional weighing construction cost, shorten the working time, and has high accuracy, which can provide technical support for the swivel of real bridge.