Recently, deep learning-based compressed sensing (CS) has achieved great success in reducing the sampling and computational cost of sensing systems and improving the reconstruction quality. These approaches, however, largely overlook the issue of the computational cost; they rely on complex structures and task-specific operator designs, resulting in extensive storage and high energy consumption in CS imaging systems. In this paper, we propose a lightweight but effective deep neural network based on recurrent learning to achieve a sustainable CS system; it requires a smaller number of parameters but obtains high-quality reconstructions. Specifically, our proposed network consists of an initial reconstruction sub-network and a residual reconstruction sub-network. While the initial reconstruction sub-network has a hierarchical structure to progressively recover the image, reducing the number of parameters, the residual reconstruction sub-network facilitates recurrent residual feature extraction via recurrent learning to perform both feature fusion and deep reconstructions across different scales. In addition, we also demonstrate that, after the initial reconstruction, feature maps with reduced sizes are sufficient to recover the residual information, and thus we achieved a significant reduction in the amount of memory required. Extensive experiments illustrate that our proposed model can achieve a better reconstruction quality than existing state-of-the-art CS algorithms, and it also has a smaller number of network parameters than these algorithms. Our source codes are available at: https://github.com/C66YU/CSRN.