Target detection technology has been greatly improved for the synthetic aperture radar (SAR) images recently, due to the advancement in deep learning (DL) domain. However, because of the existence of clutter in the SAR images, it's still a challenge to detect small targets with high accuracy and low computational complexity. To solve this problem, a detection algorithm based on feature fusion and cross-layer connection (FFCLC) network is proposed in this paper. Firstly, the attention feature fusion (AFF) is applied to improve the feature fusion ability for the small targets through allocating weights to various feature maps adaptively. Meanwhile, the depthwise separable convolution (DW-Conv) is used to reduce the computational complexity caused by the increasement of network layers. Then, a cross-layer connection (Cross-Connect) submodule is proposed to fuse shallow features with deep features further. Finally, a multi-scale target detection (Multi-Detect) submodule is designed to improve the detection ability for the small targets. We compare the proposed algorithm with the other representative methods on the SAR-Ship-Dataset and SSDD, quantitative evaluations show that our proposed algorithm's can reach the highest computational efficiency. Therefore, because of the superior performance in terms of accuracy and efficiency, the algorithm proposed in this paper is more suitable to detect small targets for the SAR images.