Brain networks classification is an important subject in brain science. In recent years, brain networks classification based on convolutional neural networks has become a hot topic. However, it is still difficult to accurately classify brain network data with high dimension and small sample size. Due to the close relationship between different clinical phenotypes and brain networks of different populations, it is highly possible to provide auxiliary information for the brain networks classification. Therefore, we propose a new brain networks classification method based on an adaptive multi-task convolutional neural network in this paper. Firstly, the clinical phenotype predictions are introduced as different auxiliary tasks and the shared representation mechanism of multi-task convolutional neural networks is used to provide general and useful information for brain networks classification. Then, in order to reduce the experimental cost and the error caused by the manual operation, a new adaptive method is proposed to substitute for manual adjustments of the weight of every task in the multi-task learning. The experimental results on the autism brain imaging data exchange I (ABIDE I) dataset show that the multi-task convolutional neural networks which introduce clinical phenotype predictions can achieve better classification results. Moreover, the adaptive multi-task learning method can further improve the performance of brain networks classification.