BACKGROUND: The workflow of prostate cancer diagnosis and grading is cumbersome and the results suffer from substantial inter-observer variability. Recent trials have shown potential in using machine learning to develop automated systems to address this challenge. Most automated deep learning systems for prostate cancer Gleason grading focused on supervised learning requiring demanding fine-grained pixel-level annotations. METHODS: A weakly-supervised deep learning model with slide-level labels is presented in this study for the diagnosis and grading of prostate cancer with whole slide image (WSI). WSIs are first cropped into small patches and then processed with a deep learning model to extract patch-level features. A graph convolution network (GCN) is used to aggregate the features for classifications. Throughout the training process, the noisy labels are progressively filtered out to reduce inter-observer variations in clinical reports. Finally, multi-center independent test cohorts with 6,174 slides are collected to evaluate the prostate cancer diagnosis and grading performance of our model. RESULTS: The cancer diagnosis (2-level classification) results on two external test sets (n= 4,675, n= 844) show an area under the receiver operating characteristic curve (AUC) of 0.985 and 0.986. The Gleason grading (6-level classification) results reach 0.931 quadratic weighted kappa on the internal test set (n= 531). It generalizes well on the external test dataset (n= 844) with 0.801 quadratic weighted kappa with the reference standard set independently. The model enables pathological meaningful interpretability by visualizing the most attended lesions which are highly consistent with expert annotations. CONCLUSION: The proposed model incorporates a graph network in weakly supervised learning with only slide-level reports. A robust learning strategy is also employed to correct the label noise. It is highly accurate (>0.985 AUC for diagnosis) and also interpretable with intuitive heatmap visualization. It can be unified with a digital pathology pipeline to deliver prostate cancer metrics for a pathology report.