To construct the exact solutions for the space-time fractional complex Ginzburg Landau equation. First, the space-time fractional complex Ginzburg Landau equation is transformed into an ordinary differential equation through fractional order complex transformation. Then, a new extended direct algebraic method is used to obtain solutions in the form of rational functions, trigonometric functions, and hyperbolic functions, respectively. The existence of these exact solutions is guaranteed by the constraints on the given parameters. This method is a simple and efficient solution method that can be widely used to solve other nonlinear partial differential equations.