We propose a novel system leveraging deep learning-based methods to predict urban traffic accidents and estimate their severity. The major challenge is the data imbalance problem in traffic accident prediction. The problem is caused by numerous zero values in the dataset due to the rarity of traffic accidents. To address the issue, we propose a grid-clustered feature map with the ideas of grids and cells. To predict the occurrence of accidents in the grid, we introduce an accident detector that combines the power of a Convolutional Neural Network (CNN) with a Deep Neural Network (DNN). Then, hierarchical DNNs are supposed to be an accident risk classifier to estimate the risk of each cell in the accident-occurrence grid. The proposed system can effectively reduce instances with no traffic accidents. Furthermore, we introduce the concept of the Accident Risk Index (ARI) to better represent the severity of risk at each cell. Also, we consider all the explanatory variables, such as dangerous driving behaviors, traffic mobility, and safety facility information, that can be related to traffic accidents. To improve the prediction accuracy, we further take into consideration all the explanatory variables, such as dangerous driving behaviors, traffic mobility, and safety facility information, that can be related to traffic accidents. In the experiment, we highlight the benefits of our method for urban traffic accident management by significantly improving model performance compared to the baselines. The feasibility and applicability of the proposed system are validated in the data of Daejeon City, Republic of Korea. The proposed prediction system can dynamically advise and recommend commuters, traffic management systems, and city planners on alternatives, optimizations, and interventions.