The main objective of this paper is to solve the problem of low resolution of target distance images obtained by GM-APD lidar. Towards overcoming this problem, this paper proposes a fractional-order super-resolution reconstruction algorithm for GM-APD lidar distance images based on convex set projection. Firstly, the first low-resolution image is upsampled three times to obtain a high-resolution reference image. Second, starting from the image degradation model, the transformation model between the low-resolution image and the high-resolution reference image is constructed. Then the high-resolution reference image is convolved using the G-L fractional order differential operator, and the estimated low-resolution image is obtained by combining the point spread function. Finally, the difference between the remaining low-resolution images and the estimated low-resolution image is calculated, and the high-resolution reference image is corrected to obtain the final high-resolution distance image. In addition to solving the edge blurring problem of the original convex set projection algorithm, the edge structure of the image is enhanced and the image quality is improved. Simulation and experimental results show that the proposed algorithm improves the information entropy by at least 24.190% and the average gradient by at least 10.812%, and achieves the super-resolution reconstruction of GM-APD LIDAR target distance images.