A reasonable geometric transformation model is the key to image registration. When the relative motion direction between the line-scan camera and the object is strictly parallel to the planar object, it is possible to align the image by using the eight-parameter geometric transformation model of the line-scan image. However, it will be invalid when the relative motion direction is arbitrary. Therefore, a new general geometric transformation model of line-scan images is proposed for line-scan image registration in this paper. Considering the different initial poses and motion directions of the line-scan camera, the proposed model is established based on the imaging model of the line-scan camera. In order to acquire line-scan images to verify the proposed model, a line-scan image acquisition system was built. The method based on feature points is used to register the line-scan images. The experimental results show that the proposed geometric transformation model can align the line-scan image collected under arbitrary relative motion direction, not just the parallel case. Besides, the statistical errors of the image feature point coordinates are the best performance after registration. The accuracy of the registration results is better than that of other existing geometric transformation models, which verifies the correctness and generality of the geometric transformation model of the line-scan camera proposed in this paper.