Abstract: Motion of an electron across an alpha magnetic mirror system with arbitray incident conditions is studied. It is found that when the central trajectory is given, any other trajectories can be distinguished as normai and abnormal ones. Electrons moving along normal trajectories accept filtering of momentum filter slit, while the others along abnormal trajectories will not. The method of computing the projections onto the central trajectory co-ordinate system of a differential arc element along normal trajectory is given, which is numerically demonstrated with enough precision. This work is of significance for understanding the details of motion of charged particle beam across alpha magnetic mirror system.