Based on the gain theory and the laser dynamic theory of laser, the effects of laser active region size, fiber grating structure, coupling efficiency and injection current on frequency noise and relaxation-oscillation frequency are analyzed, when we combine with the classical laser rate equation. To obtain low frequency noise and high relaxation oscillation frequency, a simulation is conducted. The simulation results show that a small laser active region size, a strong external cavity light feedback and a high injection current are beneficial to the improvement of noise characteristics, and the influence of injection current is especially important. When the injection current is 9 times higher than the threshold current, the frequency noise reduces by 14.7%, and the relaxation oscillation frequency increases about 6.0 GHz.