Multiple instance learning (MIL) is a typical weakly-supervised learning method where the label is associated with a bag of instances instead of a single instance. Despite extensive research over past years, effectively deploying MIL remains an open and challenging problem, especially when the commonly assumed standard multiple instance (SMI) assumption is not satisfied. In this paper, we propose a multiple instance learning method based on deep graph convolutional network and feature selection (FS-GCN-MIL) for histopathological image classification. The proposed method consists of three components, including instance-level feature extraction, instance-level feature selection, and bag-level classification. We develop a self-supervised learning mechanism to train the feature extractor based on a combination model of variational autoencoder and generative adversarial network (VAE-GAN). Additionally, we propose a novel instance-level feature selection method to select the discriminative instance features. Furthermore, we employ a graph convolutional network (GCN) for learning the bag-level representation and then performing the classification. We apply the proposed method in the prediction of lymph node metastasis using histopathological images of colorectal cancer. Experimental results demonstrate that the proposed method achieves superior performance compared to the state-of-the-art methods.