In this study, we propose a novel CNN to predict autism from functional brain networks. Experimental results demonstrate that the predictive ability of CNN outperforms a logistic regression method by 8% and a five-layer fully-connected network (FCN) by approximately 7%. Network thresholding is often used to control false connections arising in the process of constructing functional brain networks. We also compare the influence of different thresholds on the performance of proposed CNN. Experimental results show that CNN is robust to false connections. Our study will contribute to predict reliable clinical outcomes in autism using deep learning on brain networks.