Sparse synthetic aperture radar (SAR) imaging has demonstrated excellent potential in image quality improvement and data compression. However, conventional observation matrix-based methods suffer from high computational overhead, which is hard to use for real data processing. The approximated observation sparse SAR imaging method relieves the computation pressure, but it needs to manually set the parameters to solve the optimization problem. Thus, several deep learning (DL) SAR imaging methods have been used for scene recovery, but many of them employ dual-path networks. To better leverage the complex-valued characteristics of echo data, in this paper, we present a novel complex-valued convolutional neural network (CNN)-based approximated observation sparse SAR imaging method, which is a single-path DL network. Firstly, we present the approximated observation-based model via the chirp-scaling algorithm (CSA). Next, we map the process of the iterative soft thresholding (IST) algorithm into the deep network form, and design the symmetric complex-valued CNN block to achieve the sparse recovery of large-scale scenes. In comparison to matched filtering (MF), the approximated observation sparse imaging method, and the existing DL SAR imaging methods, our complex-valued network model shows excellent performance in image quality improvement especially when the used data are down-sampled.