Abstract: Stimulated by extended tanh-function method, a double functions method is proposed for constructing exact travelling wave solutions for nonlinear evolution equations. By means of the method, sixteen kinds of exact travelling wave solutions for R-L-W equation are obtained, which contain soliton wave solutions and periodic solutions. The results obtained by Zheng Bin and Zhang Hongqing are extended. With the aid of Mathematica, the method can be carried out partly by computer.