Millimeter-wave radars are being increasingly integrated into commercial vehicles to support new advanced driver-assistance systems by enabling robust and high-performance object detection, localization, as well as recognition - a key component of new environmental perception. In this paper, we propose a novel radar multiple-perspectives convolutional neural network (RAMP-CNN) that extracts the location and class of objects based on further processing of the range-velocity-angle (RVA) heatmap sequences. To bypass the complexity of 4D convolutional neural networks (NN), we propose to combine several lower-dimension NN models within our RAMP-CNN model that nonetheless approaches the performance upper-bound with lower complexity. The extensive experiments show that the proposed RAMP-CNN model achieves better average recall and average precision than prior works in all testing scenarios. Besides, the RAMP-CNN model is validated to work robustly under nighttime, which enables low-cost radars as a potential substitute for pure optical sensing under severe conditions.