The deployment of deep convolutional neural networks (CNNs) in synthetic aperture radar (SAR) ship real-time detection is largely hindered by huge computational cost. In this article, we propose a novel learning scheme for training a lightweight ship detector called Tiny YOLO-Lite, which simultaneously 1) reduces the model storage size; 2) decreases the floating point operations (FLOPs) calculation; and 3) guarantees the high accuracy with faster speed. This is achieved by self-designed backbone structure and network pruning, which enforces channel-level sparsity in the backbone network and yields a compact model. In addition, knowledge distillation is also applied to make up for the performance decline caused by network pruning. Hereinto, we propose to let small student model mimic cumbersome teacher's output to achieve improved generalization. Rather than applying vanilla full feature imitation, we redefine the distilled knowledge as the inter-relationship between different levels of feature maps and then transfer it from the large network to a smaller one. On account that the detectors should focus more on the salient regions containing ships while background interference is overwhelming, a novel attention mechanism is designed and then attached to the distilled feature for enhanced representation. Finally, extensive experiments are conducted on SSDD, HRSID, and two large-scene SAR images to verify the effectiveness of the thinner SAR ship object detector in comparison of with other CNN-based algorithms. The detection results demonstrate that the proposed detector can achieve lighter architecture with 2.8-M model size, more efficient inference (>200 fps) with low computation cost, and more accurate prediction with knowledge transfer strategy.