Autism Spectrum Disorder (ASD) is a complex neurodevelopmental disorder that impacts how people communicate, interact, behave and learn. Neuroimaging techniques including MRI have been used to not only characterize biomarkers of ASD but also identify individuals with ASD based on analyzing neural structural and functional features, which may assist the precise diagnosis of ASD especially at an early age. Most existing neuroimaging methods for ASD identification focus on a single type of neural measure such as brain functional connections, but ignore the influence of other neural features such as regional activities. There is an increasing need for computational models to use complementary information from multi-modal data for identifying mental disorders. In this work, we propose a framework of graph convolution networks (GCNs) based on maximum entropy weighted independent set pooling (MEWISPool), called MEWISPool-GCN, which not only learns the functional connections and regional activities of the entire brain network, but also integrates non-imaging data such as demographics. Specifically, the graph structure of brain imaging is first downsampled by the MEWISPool method. This structure-adaptive pooling method considers the input graph structure as a noisy communication channel to maximize the mutual information between the input nodes and the pooled nodes. Then, a population graph is constructed in order to further recalibrate the distribution of extracted features using the non-imaging phenotypic information. The feature vectors obtained after pooling are embedded into the nodes of the population graph; and the similarities between non-imaging data are used as edges connecting the nodes. GCN is then employed to learn node embeddings. In the experiment of ASD identification using ABIDE-I dataset, MEWISPool-GCN achieved an accuracy of 87.68% and AUC of 92.89%, which outperformed other related classification methods.