To develop and evaluate a method of parallel imaging time-of-flight (TOF) MRA using deep multistream convolutional neural networks (CNNs). A deep parallel imaging network ("DPI-net") was developed to reconstruct 3D multichannel MRA from undersampled data. It comprises 2 deep-learning networks: a network of multistream CNNs for extracting feature maps of multichannel images and a network of reconstruction CNNs for reconstructing images from the multistream network output feature maps. The images were evaluated using normalized root mean square error (NRMSE), peak signal-to-noise ratio (PSNR), and structural similarity (SSIM) values, and the visibility of blood vessels was assessed by measuring the vessel sharpness of middle and posterior cerebral arteries on axial maximum intensity projection (MIP) images. Vessel sharpness was compared using paired t tests, between DPI-net, 2 conventional parallel imaging methods (SAKE and ESPIRiT), and a deep-learning method (U-net). DPI-net showed superior performance in reconstructing vessel signals in both axial slices and MIP images for all reduction factors. This was supported by the quantitative metrics, with DPI-net showing the lowest NRMSE, the highest PSNR and SSIM (except R = 3.8 on sagittal MIP images, and R = 5.7 on axial slices and sagittal MIP images), and significantly higher vessel sharpness values than the other methods. DPI-net was effective in reconstructing 3D TOF MRA from highly undersampled multichannel MR data, achieving superior performance, both quantitatively and qualitatively, over conventional parallel imaging and other deep-learning methods.