Advanced 7T MR imaging improves the visualization of perivascular spaces (PVSs) in human brains. However, accurate PVS segmentation for quantitative morphological studies is still challenging, since PVSs are very thin tubular structures with low contrast in noisy MR images. We proposed a new multi-channel fully convolutional network (mFCN) to automatically segment 3D PVSs. Our mFCN method adopts multi-channel inputs to complementarily provide enhanced tubular structural information and detailed image information. Multi-scale image features are automatically learned to delineate PVSs, without requirement of any pre-defined regions of interest (ROIs). The proposed method outperforms existing automatic/semi-automatic methods with a large margin.