Abstract: In order to solve the transient electrical field in oil-paper insulation construction of converter transformer,a state equation was built based on the finite element method.The boundary conditions were combined into the equation by means of penalty method.The state space method was used to solve above equation.Firstly,the input of the equation was expanded into series,the precise numerical solution was obtained from the analytic solution in integral form.Then,an impulse function was introduced into the series expansion to simulate the step change of the boundary potential.Finally,the accuracy and validity of this method were verified with a simple model and its analytic solution.This method not only can be used to calculate the transient electric field under polarity reversal voltage in oil-paper insulation construction of converter transformer,but also can be applied to solve the heat diffusion problem and other physical problems which can be described as parabolic partial differential equations.