The principle of measuring thermospheric wind and temperature by Fabry-Perot interferometer (FPI) is elaborated, the transfer function of FPI and the analytical response expression to the incident line is studied. Referring to the basic principle of traditional wind and temperature retrieval method with FPI, a new matrix reduction technique is proposed. This technique is based on the decompose and approximate mathematics to obtain the matrix form of analytical response expression, then a least-squares technique is employed to get the thermospheric wind and temperature. Simulation results show that when the guessed wind is less than 150 m/s and the guessed temperature is less than 80 K, the error range is ±3 m/s for wind and ±10 K for temperature. The matrix technique not only retains the accuracy of a full Fourier Series Representation method, but also avoids instrument calibration and wavelength translation, which makes it simple and fast.