A cubic model of single-mode laser driven by quantum noise and nonlinear colored pump noise is founded, and the model is divided into amplitude Langevin equation (LE) and phase LE in polar coordinate. The approximate Fokker-Planck equation method is adopted to process the colored noise of phase LE, which makes the colored noise a Markovian process. Combined the equivalent phase LE which has been Markovian with phase locked conditions, the stable phase locked value is obtained. The effects of cross-correlation between the real and imaginary parts of pump noise and quantum noise on phase locked of single mode laser are discussed. Results reveal that the phase locked of laser is induced by the cross-correlation between the real and imaginary parts of quantum noise. However, the change of phase locked arises from the cross-correlation between the real and imaginary parts of pump noise or quantum noise.