In mechanical systems, assembly errors are one of the key factors affecting the operational accuracy and overall performance of the entire machine. However, at present, in the prediction of assembly errors, there is a problem that the predicted values differ greatly from the actual values, which seriously affects the assembly quality and the subsequent performance optimization. Aiming at this problem, an assembly accuracy prediction method based an improved RPM-Net and multi-constraint assembly surface weight distribution is proposed. In terms of obtaining the fit error of parts, the point cloud registration technology is adopted to precisely align the point cloud of the assembly surface, so as to obtain the geometric relationship and error information between the assembly surfaces. During the registration process, by embedding the attention mechanism into the RPM-Net framework, the network′s focus on important feature information is enhanced. This effectively suppressees the risk of registration falling into local optimum, significantly improves the registration accuracy of the assembly point cloud, and provides a more reliable data basis for the subsequent error transmission analysis. In terms of the error transmission of part fit, based on the influence degree of the end pose of each assembly surface, the torsors of the assembly surfaces that constitute multiple constraints are weighted and summed, and the torsors of non-repetitive constraints are compounded. This processing method enables comprehensive consideration of the torsors of each assembly surface, avoiding the prediction deviation caused by ignoring certain assembly surface torsors in traditional methods, and thereby improving the accuracy of assembly precision prediction. The experimental results show that the deviations between the predicted and actual values in the five degrees of freedom in space are precisely bounded within 2 μm and 4×10-5 rad. Compared with the traditional series method and algebraic operation method, the proposed method more accurately reflects actual assembly situation, providing an effective model reference for the subsequent improvement of assembly accuracy.