The measurement sensitivity can be greatly improved when tunable laser spectroscopy together with the method of wavelength modulation of second harmonic detection is used to measure the gas density. However, light transfer and circuit delay will lead to unknown phase delay. The measurement results of second harmonic signal will be seriously influenced by the phase change of the frequency-doubled reference signal relative to the measured signals containing information of gas density. A four-channel multiplier demodulation circuit is designed here. Sinusoidal signals and cosine signals are used to demodulate measured signals. Then two demodulated signals appear relating to the phase difference of sinusoidal value and cosine values after the measured signals pass the integral circuit. The amplitude signals can be obtained, which have no relation with the phase difference when demodulated signals are squared through the adder and the phase difference is eliminated. Experiment shows that the stability of the measured results in the system has been improved greatly if the obtained second harmonic signal keeps stable when the phases change from 0° to 90°.