Although fixed wavelength modulation spectroscopy has the advantage of high temporal resolution, a large measurement error of gas concentration appears with the wavenumber drift of the laser emission center. A gas concentration measurement method based on fixed wavelength modulation spectroscopy was proposed in this paper to eliminate the influence of wavenumber drift on concentration measurement. A reference optical path with a closed gas cell was introduced, and the wavenumber offset of the laser emission center was calculated according to the harmonic height. A cyclic iterative algorithm was adopted, and the gas concentration to be measured was calculated through inversion. A measurement system based on fixed wavelength modulation spectroscopy was built. The working temperature of the laser was adjusted to simulate wavenumber drift. The absorption line of CH₄ molecules near 6046.955 cm ^-1 was selected to carry out concentration measurement experiments. The results show that the maximum relative error of concentration measurement is reduced from 90.510% to 5.204%. Errors smaller than 70.000% can be controlled within 2.000% after correction. This means that the proposed method can accurately calculate the wavenumber offset, improve the measurement accuracy of gas concentration, and thereby provide technical support for fast field inversion by fixed modulation spectroscopy.