The emitting system which consists of LaB_6 cathode,Wehnelt grid and anode is one of pivotal component of X-ray source with micro-beam.The partition mode and equations of BEM to deal with LaB_6 cathode electronic gun were detailedly discussed in the paper,in order to enhancing precision of solution,quadric isoparametric interpolation method was used.Likewise,the axile potential and intensity of the system were calculated by Gauss elimination method and cubic spline interpolation.Furthermore,the electronic trajectory was traced by the changing steps Runge-Kutta method,the final size of e-beam about anode was true of demand.