Based on tanh-function method, homogeneous balance method and auxiliary equation, a new auxiliary equation was introduced in the paper, meanwhile, a new invariance solution was obtained, and a new exact solitary wave solution for Benjamin-Bona-Mahoney(BBM) equation and modified BBM equation was constructed using the symbolic calculation system of Mathematica. The method introduced in the paper has general significance in searching for exact solutions to the nonlinear developing equation.