The distortion in the imaging of space-based optical cameras for actual in-orbit earth observations needs to be suppressed by geometric correction. At present, the small size and high frame rate sequential images obtained by mainstream area array cameras for ground observation are difficult to meet the requirements of traditional geometric correction methods for calculating the number of control points and spatial distribution of frame-by-frame solution, and the computational complexity is huge. To address this issue, a geometric correction method by using equivalent bias angle sparse measurement for sequential observation image of area-array sensor was proposed. The problem of parameters solution for each frame converted to the problem of equivalent bias angle recovery under the time-domain sparse measurement. The requirement for the number and spatial distribution of control points in a single frame image were reduced by using the time-frequency information of equivalent bias angle signal. Meanwhile, the real image data from the area-array camera of Gaofen-4 satellite was used to verify the validity and low computation of the proposed method.