The exact solution of space-time fractional complex Ginzburg-Landau equation is studied. Firstly, fractional complex transformation is applied to the space-time fractional complex Ginzburg-Landau equation, it is transformed from fractional partial differential equation to ordinary differential equation. Then, a new extended direct algebraic method is used to obtain solutions,which are given in the form of rational function, trigonometric function and hyperbolic function respectively. The existence of these exact solutions is guaranteed by the constraints on the given parameters. The method is simple and effective, and can be applied to the solution of other nonlinear partial differential equations.