The numerical simulation process of bolted flange joints involves many contact pairs, and the difficulty in the convergence of numerical simulation commonly exists for contact problem. Taking the finite element analysis for the flange joints of geared compressor by ANSYS workbench as an example, we analyzed the main factors influencing computational convergence in detail, including the construction of contact pairs, the determination of contact type, the selection of proper algorithm and the value of F_KN(contact stiffness factor). In the process of simulation, unsymmetrical bonded contact was applied to the connection between nuts and bolts, and unsymmetrical frictional contact was applied to the contact on two flange surfaces and the connection between nuts and flanges. Moreover, the screwing of bolts was simulated by applying bolt pretension in linear. In the process of the numerical computation, pure penalty and augmented Lagrangian were applied to the bonded contact and the frictional contact, respectively. with a small F_KN in the inifial computation, it was gradually increased according to the result of the contact iteration and N-R residual until the computation converged. The convergence of the example is well, the frictional stress on the contact surfaces conforms to the distribution of compression stress and there is only very small slide on the contact surfaces, so the computation result meets engineering utilization requirements. At the same time, it offers some reference to resolve the convergence problem of other's contact type.