Synthetic Aperture Radar (SAR) scene classification is challenging but widely applied, in which deep learning can play a pivotal role because of its hierarchical feature learning ability. In the paper, we propose a new scene classification framework, named Feature Recalibration Network with Multi-scale Spatial Features (FRN-MSF), to achieve high accuracy in SAR-based scene classification. First, a Multi-Scale Omnidirectional Gaussian Derivative Filter (MSOGDF) is constructed. Then, Multi-scale Spatial Features (MSF) of SAR scenes are generated by weighting MSOGDF, a Gray Level Gradient Co-occurrence Matrix (GLGCM) and Gabor transformation. These features were processed by the Feature Recalibration Network (FRN) to learn high-level features. In the network, the Depthwise Separable Convolution (DSC), Squeeze-and-Excitation (SE) Block and Convolution Neural Network (CNN) are integrated. Finally, these learned features will be classified by the Softmax function. Eleven types of SAR scenes obtained from four systems combining different bands and resolutions were trained and tested, and a mean accuracy of 98.18% was obtained. To validate the generality of FRN-MSF, five types of SAR scenes sampled from two additional large-scale Gaofen-3 and TerraSAR-X images were evaluated for classification. The mean accuracy of the five types reached 94.56%; while the mean accuracy for the same five types of the former tested 11 types of scene was 96%. The high accuracy indicates that the FRN-MSF is promising for SAR scene classification without losing generality.