Variable-rate mechanism has improved the flexibility and efficiency of learning-based image compression that trains multiple models for different rate-distortion tradeoffs. One of the most common approaches for variable-rate is to channel-wisely or spatial-uniformly scale the internal features. However, the diversity of spatial importance is instructive for bit allocation of image compression. In this paper, we introduce a Spatial Importance Guided Variable-rate Image Compression (SigVIC), in which a spatial gating unit (SGU) is designed for adaptively learning a spatial importance mask. Then, a spatial scaling network (SSN) takes the spatial importance mask to guide the feature scaling and bit allocation for variable-rate. Moreover, to improve the quality of decoded image, Top-K shallow features are selected to refine the decoded features through a shallow feature fusion module (SFFM). Experiments show that our method outperforms other learning-based methods (whether variable-rate or not) and traditional codecs, with storage saving and high flexibility.