There are obvious geometric nonlinear mechanical characteristics in new type arch bridge with diagonal web cables. Meanwhile, the convergence of the existing arch axis iterative optimization method is not good. In order to solve new type arch bridge axis iteration convergence problem considering geometric nonlinear mechanical analysis, an arch axis iteration optimization method was proposed based on the iteration basis finite element model with two hinge arch model in main arch ring. A 600m span arch bridge with diagonal web cables was selected as an example to test the convergence performance and applicability of proposed method. The results showed that the bending moment of proposed method had better distribution along arch span, and it is about 35% smaller in maximum bending moment, 17% smaller in minimum bending moment and 23% smaller in bending strain energy compared to the results of linear iteration optimization method. Convergence analysis results demonstrated that proposed method had better iteration performance than the existing method. Meanwhile, different initial arch axis can converge to stable results.