Inverse synthetic aperture radar(ISAR) plays an important role in radar target recognition, space surveillance, and ballistic missile defense. Considering that the traditional sparse aperture ISAR imaging algorithms are extremely sensitive to parameters and have slow convergence speed, this paper proposed a sparse aperture ISAR imaging recovery method based on complex valued-fast iterative shrinkage thresholding algorithm (CV-FISTA) network. This method first introduced the accelerated proximal gradient method into the sparse reconstruction algorithm and constructd its iterative steps into a hidden layer of the deeply unfolded network. Then, a dataset of random scattering points and aircraft scattering points with the same initial parameters was constructed, the complex one-dimensional distance image was used as the input of the network that was trained and verified by using the corresponding label of the ISAR image. Defterent from the traditional two-way calculation method including real and imaginary parts, this method directly processes comptex data, and therefore significantly reduces the computational burden. Compared with the traditional model-driven algorithm, simulation experiments verify that the proposed method can avoid setting parameters manually by training network, and have faster convergence speed, higher imaging quality, and better generalization ability for data with large feature differences.