Abstract: A numerical method solving the point reactor neutron kinetics equation by using the technique of second-order Taylor polynomials for the approximation of the neutron density in integral of one step was presented and optimized. The stiffness of the equations was overcome by the full implicit formulation. The numerical results show that for reasonable reactivity inputs, a sufficient accuracy can be achieved in Taylor polynomial approach presented here. When the reactivity is given, this method can provide a straight forward computation procedure for solving reactor dynamics problems quickly. And this method is more accuracy after amended. This numerical method can be used to the design analysis and simulation computation of reactor control.