Dense depth completion is essential for autonomous driving and robotic navigation. Existing methods focused on attaining higher accuracy of the estimated depth, which comes at the price of increasing complexity and cannot be well applied in a real-time system. In this paper, a coarse-to-fine and lightweight network (S&CNet) is proposed for dense depth completion to reduce the computational complexity with negligible sacrifice on accuracy. A dual-stream attention module (S&C enhancer) is proposed according to a new finding of deep neural network-based depth completion, which can capture both the spatial-wise and channel-wise global-range information of extracted features efficiently. Then it is plugged between the encoder and decoder of the coarse estimation network so as to improve the performance. The experiments on KITTI dataset demonstrate that the proposed approach achieves competitive result with respect to state-of-the-art works but via an almost four times faster speed. The S&C enhancer can also be easily plugged into other existing works to boost their performances significantly with negligible additional computations.