Synthetic aperture radar (SAR) automatic target recognition (ATR) plays an important role in SAR image interpretation. However, at least hundreds of training samples are usually required for each target type in the existing SAR ATR algorithms. In this article, a novel few-shot learning framework named hybrid inference network (HIN) is proposed to tackle the problem of SAR target recognition with only a few training samples. The recognition procedure of HIN consists of two main stages. In the first stage, an embedding network is utilized to map the SAR images into an embedding space. In the second stage, a hybrid inference strategy that combines the inductive inference and the transductive inference is adopted to classify the samples in the embedding space. In the inductive inference section, each sample is recognized independently according to a metric based on Euclidean distance. In the transductive inference section, all samples are recognized as a whole according to their manifold structures by label propagation. Finally, in the hybrid inference section, the classification result is obtained by combining the above two inference methods. To train the framework more effectively, a novel loss function named enhanced hybrid loss is proposed to constrain samples to gain better interclass separability in the embedding space. Experimental results on the moving and stationary target acquisition and recognition (MSTAR) benchmark data set illustrate that HIN performs well in few-shot SAR image classification.