In the paper, we propose a time-splitting high-order compact alternating direction implicit (ADI) finite difference scheme for two-dimensional complex Ginzburg-Landau (GL) equation. The GL equation is split into a nonlinear sub-problem and two linear sub-problems. The nonlinear sub-problem and one of the linear subproblems are solved exactly. Then a compact alternating direction implicit difference scheme is constructed for another linear subproblem. In practical computation, a family of constant coefficient tri-diagonal linear algebraic equations by using the catch-up method at each time step is solved to make the algorithm get high accuracy and efficiency. Numerical experiments show that the algorithm has second-order and fourth-order accuracy in time and space direction, respectively. And some dynamics behaviors of the equation are simulated.