As an active microwave imaging sensor for the high-resolution earth observation, synthetic aperture radar (SAR) has been extensively applied in military, agriculture, geology, ecology, oceanography, etc., due to its prominent advantages of all-weather and all-time working capacity. Especially, in the marine field, SAR can provide numerous high-quality services for fishery management, traffic control, sea-ice monitoring, marine environmental protection, etc. Among them, ship detection in SAR images has attracted more and more attention on account of the urgent requirements of maritime rescue and military strategy formulation. Nowadays, most researches are focusing on improving the ship detection accuracy, while the detection speed is frequently neglected, regardless of traditional feature extraction methods or modern deep learning (DL) methods. However, the high-speed SAR ship detection is of great practical value, because it can provide real-time maritime disaster rescue and emergency military planning. Therefore, in order to address this problem, we proposed a novel high-speed SAR ship detection approach by mainly using depthwise separable convolution neural network (DS-CNN). In this approach, we integrated multi-scale detection mechanism, concatenation mechanism and anchor box mechanism to establish a brand-new light-weight network architecture for the high-speed SAR ship detection. We used DS-CNN, which consists of a depthwise convolution (D-Conv2D) and a pointwise convolution (P-Conv2D), to substitute for the conventional convolution neural network (C-CNN). In this way, the number of network parameters gets obviously decreased, and the ship detection speed gets dramatically improved. We experimented on an open SAR ship detection dataset (SSDD) to validate the correctness and feasibility of the proposed method. To verify the strong migration capacity of our method, we also carried out actual ship detection on a wide-region large-size Sentinel-1 SAR image. Ultimately, under the same hardware platform with NVIDIA RTX2080Ti GPU, the experimental results indicated that the ship detection speed of our proposed method is faster than other methods, meanwhile the detection accuracy is only lightly sacrificed compared with the state-of-art object detectors. Our method has great application value in real-time maritime disaster rescue and emergency military planning.