GF-7 satellite is equipped with the first laser earth observation altimeter with full waveform recording ability in China, which can obtain a wide range of high-precision three-dimensional coordinates, and its positioning accuracy is highly dependent on the measurement accuracy of laser pointing angle. According to the characteristics of data, a centroid extraction algorithm of ellipse fitting spot with threshold constraint was proposed, and a long-period pointing angle stability monitoring system was established. Firstly, the threshold method was used to determine the edge of the laser spot contour. Secondly, the influence of porosity and noise was eliminated through corrosion operation. Then, the shape of the laser spot was further constrained by ellipse fitting, and the characteristic parameters of the laser spot were preserved. Finally, the centroid coordinates were extracted by using the gray gravity center method. The experimental results show that the centroid position of the spot changes within 1.4 pixel, and the corresponding pointing angle changes within 0.434″ per month, which is relatively stable. The related algorithms and conclusions in this paper have certain reference significance for the development of laser altimetry satellites and the monitoring of pointing stability in China.