To achieve precise measurement of micro angle, a method of angular displacement measurement based on least square fitting wave vector estimation is proposed , the method uses the holographic theory and sampling theorem to record two holograms by secondary exposure, and calculates the relative parameters of the measured optical phase information by angle spectrum analysis, estimates the angular displacement relationship between the two wave vectors. The feasibility and accuracy of this method are verified by computer simulation, and the effects of pixel size, pixel number, and signal-to-noise ratio on measurement accuracy are analyzed. The consistency between theoretical calculation results and experimental results is verified by experiments. The experiment shows that when the number of CCD pixels is not less than 1000 pixels, the pixel size is not less than 4.6 μm, and the signal-to-noise ratio is not less than 20dB, the measurement method can achieve accurate measurement within the range of 3.9 °, and the mean error of measurement is controlled within 2.5×10-7rad, the standard deviation of measurement was controlled within 2.0×10-7rad.