Multi-parameter magnetic resonance imaging (mp-MRI) is increasingly popular for prostate cancer (PCa) detection and diagnosis. However, interpreting mp-MRI data which typically contains multiple unregistered 3D sequences, e.g. apparent diffusion coefficient (ADC) and T2-weighted (T2w) images, is time-consuming and demands special expertise, limiting its usage for large-scale PCa screening. Therefore, solutions to computer-aided detection of PCa in mp-MRI images are highly desirable. Most recent advances in automated methods for PCa detection employ a handcrafted feature based two-stage classification flow, i.e. voxel-level classification followed by a region-level classification. This work presents an automated PCa detection system which can concurrently identify the presence of PCa in an image and localize lesions based on deep convolutional neural network (CNN) features and a single-stage SVM classifier. Specifically, the developed co-trained CNNs consist of two parallel convolutional networks for ADC and T2w images respectively. Each network is trained using images of a single modality in a weakly-supervised manner by providing a set of prostate images with image-level labels indicating only the presence of PCa without priors of lesions' locations. Discriminative visual patterns of lesions can be learned effectively from clutters of prostate and surrounding tissues. A cancer response map with each pixel indicating the likelihood to be cancerous is explicitly generated at the last convolutional layer of the network for each modality. A new back-propagated error E is defined to enforce both optimized classification results and consistent cancer response maps for different modalities, which help capture highly representative PCa-relevant features during the CNN feature learning process. The CNN features of each modality are concatenated and fed into a SVM classifier. For images which are classified to contain cancers, non-maximum suppression and adaptive thresholding are applied to the corresponding cancer response maps for PCa foci localization. Evaluation based on 160 patient data with 12-core systematic TRUS-guided prostate biopsy as the reference standard demonstrates that our system achieves a sensitivity of 0.46, 0.92 and 0.97 at 0.1, 1 and 10 false positives per normal/benign patient which is significantly superior to two state-of-the-art CNN-based methods (Oquab et al., 2015; Zhou et al., 2015) and 6-core systematic prostate biopsies.