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The geometric correction of the CCD images of HJ-1A/B has been a challenging job since September 6, 2008, when the satellites were launched in China, because of the special imaging geometry of bigger aspect angle and wider swath width. In this paper, the author determines to analyse the global and local distortions of the HJ-1A/B CCD system geometric correction products, and give the ways on how to correct them by using three mathematical models for test. The models include polynomial model, thin plate splines, and finite element method. The results show that: (1) both global system distortions and complex local distortions exist within the CCD images; (2) polynomial model gets the worst accuracy; (3) thin plate splines significantly improve accuracy, but the RMSE is still over 2 pixels. (4) the finite element method is recommended to be used of precise geometric correction for HJ-1A/B CCD imagery if the control points are enough and evenly distributed. Besides it is a local method, and possesses the advantages of rapidity and stability.