Light intensity fluctuations and phase randomness in quadrature demodulation disturb the accuracy of frequency modulation spectroscopy. The proposed self-corrected method eliminated these effects: the profile of correctly demodulated signals identified whether a demodulation was phase matched and corrected a phase-mismatched demodulated signal; we extracted the measured signal's direct current component and corrected the light intensity fluctuation. We conducted theoretical analysis and experimental verification to reduce light-intensity errors by 16.8% under different intensity conditions and obtained spectral features by phase difference corrections under the same measurement conditions. We reduced the effect of light intensity fluctuation and demodulated signals were freed from phase stability limitations.