The ECR microwave discharge ischarge is studied numerically with a particle model using an one dimensional electromagnetic particle-in-cell Monte-Carlo collision method (PIC-MCC mothod). In our model, the electromagnetic wave is polarized circularly and propagates along an external static magnetic field and elastic, excitational and ionizing electron-neutral collisions and elastic and charge exchange ion-neutral collisions are included. The motions of charged particles are determined by the equations of motion and collision processes. The electomagnetic fields are calculated through Maxwell``s equations. The discharge for helium gas is simulated and the simulation results explain well the physical properities of the ECR discharge which include the energy absorption of electrons through ECR coupling, the propagation of microwave, the transports of the charged particles and the effect of divergent extermal magnetic field.