Few-shot classification aims to learn a well performance model with very limited labeled examples. There are mainly two directions for this aim, namely, meta- and metric-learning. Meta learning trains models in a particular way to fast adapt to new tasks, but it neglects variational features of images. Metric learning considers relationships among same or different classes, however on the downside, it usually fails to achieve competitive performance on unseen boundary examples. In this paper, we propose a Meta Generalized Network (MGNet) that aims to combine advantages of both meta- and metric-learning. There are two novel components in MGNet. Specifically, we first develop a meta backbone training method that both learns a flexible feature extractor and a classifier initializer efficiently, delightedly leading to fast adaption to unseen few-shot tasks without overfitting. Second, we design a trainable adaptive interval model to improve the cosine classifier, which increases the recognition accuracy of hard examples. We train the meta backbone in the training stage by all classes, and fine-tune the meta-backbone as well as train the adaptive classifier in the testing stage.