Functional derivation is employed to analyze the two-dimensional colored noise in the third-order laser model. The stationary intensity distribution is derived. The variation of the most probable intensity with pump parameter and noise intensity correlation time is investigated. With the shifted 1/N expansion, the instantaneous solution of the laser model, i.e., the change of eigenvalues with the pump parameter, is obtained. It is shown that the pump parameter and intensity noise correlation time are the major factors of the first-order-like transition. Angular noise correlation time has great influence on the linewidth in the intensity spectrum.