For the numerical simulation method of the dynamic launching in electromagnetic rail launcher, a discrete formulation of three dimensional transient eddy problem for electromagnetic rail launcher considering dynamic launching was established, based on the magnetic vector A and the time integrated electrical scalar potential V, combined by using nodal element method and the moving coordinate frame to deal with the motion. The corresponding three dimensional magneticthermal coupled model was formed finally by using the governing equation for thermal field. The dynamic launching process of an electromagnetic rail launcher was simulated by the finite element model. Numerical analysis results of FEM (finite element method) code and the experiment results were compared and analyzed. The characteristic of thermal field distribution for launcher and the variation of inductance gradient with time were obtained by the model. Results show that the magnitudes of the pulsed current, muzzle current, and muzzle velocity have good correspondence with measure dates respectively, which has verified the correctness of the FEM code.