This paper discuss a new approach of $(G'/G)$-expansion method for constructing more general exact solutions of nonlinear fractional Klein-Gordon equation. By using the fractional complex transformation,the nonlinear fractional Klein-Gordon equation have been converted to nonlinear ordinary differential equation,we will apply the extended $(G'/G)$-expansion method to construct the exact solutions of nonlinear fractional Klein-Gordon equation,a series new explicit solutions were obtained,which include hyperbolic function,trigonometric and negative exponential solutions,more richer than before results.
