In this paper, a method for measuring laser wavelength stability with the FMCW interferometric cavity is proposed, which uses the advantages of high precision, high resolution, and real time measurement of FMCW interference to solve the quantification problem of laser wavelength stability. By deducing the theory underlying the interferometric cavity measurement method, the demodulation algorithm of wavelength drifts is designed to realize the real time measurement of laser wavelength drifts and effectively improve the measurement resolution of wavelength drifts. The experimental results show that the measurement resolution of wavelength shift of the proposed method is 0.016 pm, the calculation speed of wavelength shifts is up to 50/s, and the measurement time is 0.02 s. Compared with those of the optical beating method and interference comparator method, the measurement speed is greatly improved. The laser shows an average wavelength stability of 0.19×10^-6 within 1 h. This stability is better than that of most dual-frequency lasers on the market . The proposed method is of great significance to the research on improving the accuracy of FMCW interferometry and has good application value in the field of laser wavelength stability measurements.