Small UAV target detection plays an important role in maintaining the security of cities and citizens. UAV targets have the characteristics of low-altitude flights, slow speeds, and miniaturization. Taking these characteristics into account, we present a real-time UAV target detection algorithm called Fast-YOLOv4 based on edge computing. By adopting Fast-YOLOv4 in the edge computing platform NVIDIA Jetson Nano, intelligent analysis can be performed on the video to realize the fast detection of UAV targets. However, the current iteration of the edge-embedded detection algorithm has low accuracy and poor real-time performance. To solve these problems, this paper introduces the lightweight networks MobileNetV3, Multiscale-PANet, and soft-merge to improve YOLOv4, thus obtaining the Fast-YOLOv4 model. The backbone of the model uses depth-wise separable convolution and an inverse residual structure to simplify the network’s structure and to improve its detection speed. The neck of the model adds a scale fusion branch to improve the feature extraction ability and strengthen small-scale target detection. Then, the predicted boxes filtering algorithm uses the soft-merge function to replace the traditionally used NMS (non-maximum suppression). Soft-merge can improve the model’s detection accuracy by fusing the information of predicted boxes. Finally, the experimental results show that the mAP (mean average precision) and FPS (frames per second) of Fast-YOLOv4 reach 90.62% and 54 f/s, respectively, in the workstation. In the NVIDIA Jetson Nano platform, the FPS of Fast-YOLOv4 is 2.5 times that of YOLOv4. This improved model performance meets the requirements for real-time detection and thus has theoretical significance and application value.