In this paper, by establishing a tri-mode rate equation model with a gain spectrum model and Langevin noise sources, the relative intensity noise, frequency noise and linewidths of a WGM microcavity laser are investigated numerically, and the influence of the mode competition on noise characteristics of the microcavity lasers is mainly studied.The steady-state characteristics of the microcavity laser are simulated by the tri-mode rate equation model including carrier densities, photon densities and mode phases. The mode skipping due to the thermal effect caused by the injection current is simulated. As the temperature increases due to the current injection, the lasing wavelength of the microcavity laser redshifts and the mode skips with the increase of the injection current. The effect on the optical power, relative intensity noise, frequency noise and linewidths are studied by inducing Langevin noise sources to the rate equations. When the microcavity laser is at a single-mode lasing state, the relaxation oscillation peaks of the relative intensity noise and frequency noise spectra both move to the high frequency with the increase of the injection current, and the whole relative intensity noise and frequency noise decrease. Relative intensity noise refers to the ensemble average of the fluctuations of the laser power relative to the average power squared. The relative intensity noise approaches the standard quantum limit of -165.5 dB/Hz at a high bias current of 115 mA, a long integral time of 50 μs and a short time step of 1 ps. The frequency noise of the laser refers to the random fluctuation of instantaneous mode frequency, which comes from the natural phase noise of the laser caused by the spontaneous emission, and phase noise caused by carrier fluctuation. And the linewidth of the microcavity laser, which is the full-width at half-maximum of the single-mode spectrum, is determined from the low-frequency of the frequency noise spectrum. By averaging the frequency noise at the low-frequency of the frequency noise spectrum, a low linewidth of 85.6 kHz for the microcavity laser could be obtained with I=115 mA and Q=2.5×10⁴, which is smaller than the measured laser linewidth.Furthermore, the fast Fourier transform is proposed to simulate the laser spectrum using the mode electric field expressed by the mode photon density and the mode phase. When the injection current is 115 mA and the integral time is 50 μs, the optical spectrum of the laser line shape is obtained and the simulated linewidth of the microcavity laser by Lorentz fitting is 77.2 kHz, which is about 10% smaller than that obtained from the frequency noise spectrum.When the microcavity laser is dual-mode lasing, the relative intensity noise and the frequency noise of each mode increases obviously at the low-frequency due to the mode competition. When the injection current is 51 mA, the microcavity laser is dual-mode lasing at modes M1 and M2. The relative intensity noise at low-frequency increases by 25 dB/Hz, and the linewidths of the two modes with output powers of 3.33 mW and 1.63 mW, calculated from the frequency noise spectrum at low frequency, are 1.5 times and 6 times of the linewidth at single-mode lasing state with the same output power. The linewidths of the dual-mode lasing state are significantly widened, which is consistent with the experimental results. The mode electric field is also analyzed with the help of the fast Fourier transform and the laser linewidths obtained from the lasing mode spectra are in agreement with those obtained from the frequency noise spectra. The dynamic change process of the frequency noise and the linewidth at dual-mode lasing state are studied when the injection current varies from 50 to 52 mA. When the side-mode suppression ratio is less than 20 dB, the laser linewidth begins to widen. The frequency noise at low-frequency of the high power state mode rises faster than that at high-frequency, and the frequency noise at low-frequency of the low power mode falls slower than that at high-frequency, which makes the frequency noise at low-frequency of the microcavity laser always in a high state and widens the linewidth of the microcavity laser .