In order to improve the accuracy of cavity length demodulation of Extrinsic Fabry-Perot Interferometric (EFPI), a demodulation method based on the approximate cosine function of the reflection spectrum was designed based on Lissajous-Figure and standard elliptic curve fitting. The two sets of light intensity signals were fitted into standard elliptic curves by coordinate transformation to reduce the required parameters; The empirical mode decomposition was used to analyze the data. The extreme point obtained after the baseline was taken into the elliptic curve to solve the problem. The discrete data points were moved by 5, 10, 15, 20 and 25 points respectively to test the influence of five groups of different phase shifts on the demodulation results, and the group with the smallest error was selected for the transverse load experiment of EFPI sensor. The stress of 5-25 N was applied respectively, the calculated cavity length difference was compared with the theoretical cavity length difference by the demodulation method of fitting elliptic curve. The results show that the actual cavity length difference is proportional to the load, the average error is about 5.690%, and the cavity length of EFPI can be obtained accurately.