The regularization-based approaches offer promise in improving synthetic aperture radar (SAR) imaging quality while reducing system complexity. However, the widely applied l1 regularization model is hindered by their hypothesis of inherent sparsity, causing unreal estimations of surface-like targets. Inspired by the edge-preserving property of total variation (TV), we propose a new complex-valued TV (CTV)-driven interpretable neural network with nested topology, i.e., CTV-Net, for 3-D SAR imaging. In our scheme, based on the 2-D holography imaging operator, the CTV-driven optimization model is constructed to pursue precise estimations in weakly sparse scenarios. Subsequently, a nested algorithmic framework, i.e., complex-valued TV-driven fast iterative shrinkage thresholding (CTV-FIST), is derived from the theory of proximal gradient descent (PGD) and FIST algorithm, theoretically supporting the design of CTV-Net. In CTV-Net, the trainable weights are layer-varied and functionally relevant to the hyperparameters of CTV-FIST, which aims to constrain the algorithmic parameters to update in a well-conditioned tendency. All weights are learned by end-to-end training based on a two-term cost function, which bounds the measurement fidelity and TV norm simultaneously. Under the guidance of the SAR signal model, a reasonably sized training set is generated, by randomly selecting reference images from the MNIST set and consequently synthesizing complex-valued label signals. Finally, the methodology is validated, numerically and visually, by extensive SAR simulations and real-measured experiments, and the results demonstrate the viability and efficiency of the proposed CTV-Net in the cases of recovering 3-D SAR images from incomplete echoes.