Abstract: The Taylor expansion approximate method is deScribed with the precision of the second order, which is used to solve the electrostatic Poisson equation in the region with arbitrary shape. The Roberta rule is applied to obtain the potential distribution on the axisymmetric axle of the physical problem. A set of universal formulae is derived to solve the problem with various,boundary, so that the complexity of the problem is avoided and the simulating code can be simplied much more.