Few-shot classification aims to identify novel categories using only a few labeled samples. Generally, the metric-based few-shot classification methods compare the feature embedding of Query samples (unlabeled samples) with Support samples (labeled samples) in a metric algorithm to predict which category the Query sample belongs to. Obtaining a good feature embedding for each sample in the feature extraction stage can improve the classification accuracy in the metric stage. Based on this, we design the Self-Guided Information Convolution (SGI-Conv), an improved convolution structure, which utilizes the high-level features to guide the network to extract the required discriminative features. To effectively utilize the feature embeddings of samples, we divide the metric network into multiple blocks and build a multi-layer graph convolutional network by sharing adjacent matrices. The multi-layer structure enhances the aggregation ability of graph convolution. Extensive experiments on multiple benchmark datasets demonstrate that our method has achieved competitive results on the few-shot classification tasks.