The HaiYang-1C (HY-1C) ultra violet imager (UVI) consists of five independent cameras with a designed total image swath of approximately 3000 km. In order to obtain a complete seamless image formed by the five sub-images, a feasible geometric stitching method for the HY-1C UVI with a distorted virtual camera is proposed. First, we perform the absolute geometric calibration of camera 3 and the relative geometric calibration of cameras 1, 2, 4, and 5. Then, a distorted virtual camera is assigned. Finally, the five sub-images are stitched together with the distorted virtual camera. Three HY-1C UVI images were tested. The experimental results showed that the georeferencing accuracy of the stitched images was better than 1 pixel. Compared with the conventional stitching method with an undistorted virtual camera, the ground sampling distance differences of the five cameras obtained by the proposed method were reduced from 23%, 37%, 53%, 37%, and 25% to 6%, 6%, 1%, 7%, and 8%, respectively.