Radar signal-based object detection has become a primary and critical issue for autonomous driving recently. Recently advanced radar object detectors indicated that the cross-model supervisionbased approach presented a promising performance based on 3D hourglass convolutional networks. However, the trade-off between computational efficiency and performance of radar object detection tasks is rarely investigated. When higher performance is required in the detection tasks, the 3D convolutional backbone network rarely meets the real-time applications. This paper proposes a lightweight, computationally efficient, and effective network architecture to conquer this issue. First, Atrous convolution, as well-known as dilated convolution, is adopted in our backbone network to make a smaller convolutional kernel having a larger receptive field so as a larger convolutional kernel can be eliminated to reduce the number of parameters. Furthermore, a densely connected residual block (DCSB) is proposed to better deliver the gradient flow from the loss function to improve the feature representation ability. Finally, the hourglass network structure is made by stacking several DCSBs with Mish activation function to form our detection network, termed as DCSN. In this manner, we can keep a larger receptive field and reduce the number of parameters significantly, resulting in an efficient radar object detector. Experiments are demonstrated that the proposed DCSN achieves a significant improvement of inference time and computational complexity, with comparable performance for radar object detection. The source code can be found in https://github.com/jesse1029/RADER-DCSN.