Autism Spectrum Disorder (ASD) is a neurodevelopmental disease which can cause social handicap, communication and behavior disorders. Up to now, many machine learning methods have been proposed for ASD diagnosis using multisite resting-state functional magnetic resonance imaging(rs-fMRI) data. However, above these methods still exist two main challenging problems: the data heterogeneity (e.g. caused by different scanners and parameters, subject populations) among multiple sites and the difficult to handle the graph-based functional connectivity networks. To simultaneously address two challenging problems, in this paper, we propose a graph convolutional network via low-rank subspace (LRGCN) method for ASD diagnosis using multi-site rs-fMRI data. First, to alleviate the data heterogeneity, the low rank representation(LRR) learning is introduced to learn a low rank subspace from multiple sites. Then, LRGCN method employs graph convolutional networks(GCN) to discovery the more useful features from graph-based functional connectivity networks, which are constructed by the low-rank subspace. We evaluate our LRGCN method on the public Autism Brain Imaging Data Exchange (ABIDE) database. Experimental results demonstrate that our method improve the performance of ASD diagnosis, and outperforms four baseline and three state-of-the-art methods. In addition, the LRGCN provides an universal framework which can be extended to diagnosis various human diseases using multi-site rs-fMRI data.