The target edge contains the shape and structure information of the target. Accurate extraction of target edges is the basis of target recognition and location. The number of pixels and signal-to-noise ratio severely limit the edge extraction capability of single-photon lidar. In this work, a target edge extraction algorithm for array single-photon lidar is proposed based on the distribution characteristics of the target edge echo waveform. The algorithm does not need to image the target or rely on the fixed direction edge detection template. The target edge is divided into the inside and outside edges based on the established target edge echo signal model of array single-photon lidar. Single and double Gaussian function fitting is used to extract the outside edge whose echo waveform is a double pulse distribution. The feature vector composed of skewness, FWHM, and total detection probability of the echo waveform is weighted K-means clustered to extract the inside edge whose echo waveform is a single pulse distribution. Screening misjudged pixels based on the Jensen-Shannon divergence between echo waveforms of each pixel to improve the edge extraction accuracy. Simulation and experimental results demonstrate that the proposed algorithm can extract target edges more completely and accurately than traditional edge extraction methods. The minimum inside edge depth of the target that the proposed algorithm can extract is cτ/2, where τ is the standard deviation of the emitted Gaussian laser pulse. This research has the potential to improve the target detection and recognition capabilities of array single-photon lidar.