We have established a model for the analysis of azimuthal-radial pendulum by Lagrangian mechanics. We list the I agrangian function of the system and consider the influence of air resistance. The theoretical trajectory of the azimuth-radial pendulum is obtained by numerical simulation.The influence of the weight' s mass , the releasing azimuth angle and the releasing radial angle on the maximum displacement in the direction of azimuth was investigated by using the method of controlling variables.The experimental results were in good agreement with the numerical simulation results , which further proved the correctness of our theory.