The core imaging spectrometer developed by Nanjing Center of China Geological Survey consisted of a visible near infrared (VNIR) imaging spectrometer, a short wave infrared (SWIR) imaging spectrometer and a guide railway on which the core plate was mounted. The control accuracy of the uniform-speed moving guide railway and the different spatial resolutions and fields of view (FOV) of the VNIR imaging spectrometer and the SWIR imaging spectrometer caused geometric distortions on the core data. So the data obtained cannot be directly used for subsequent applications. In the face of these potential problems, on the basis of analysis error mechanism, geometric correction method based on the triangle calibration and joint image registration method of pixel and sub-pixel level were proposed. By setting triangle calibration target on one side of a core plate, geometric stretch and compression distortion was detected and corrected. By introducing scale invariant feature transform and extensible phase correlation, registration accuracy was improved. Experimental results using core hyperspectral data produced by Nanjing Center of China Geological Survey show that this improved geometric correction method can achieve a stretch and compression correction accuracy of 0.28 pixel and registration accuracy better than 0.1 pixel.