Compressive hyperspectral imaging is an emerging technology that captures compressed two-dimensional (2D) measurements and subsequently reconstructs three-dimensional (3D) hyperspectral images, capitalizing on the sparsity prior. Numerous end-to-end networks have been proposed, yielding notable improvements in reconstruction speed and quality compared to traditional algorithms. However, these networks fall short in exploiting the sparsity of hyperspectral images in their direct mapping from 2D measurements to 3D hyperspectral images. To address this limitation, this paper introduces a novel approach for compressive hyperspectral image reconstruction using deep learning. The deep learning network comprises two components: the sparse coefficient recovery net and the dictionary training net. The dictionary training net incorporates a pre-trained dictionary, whose parameters can also be updated during the backpropagation process. Concurrently, the sparse coefficient recovery net generates sparse coefficients under this dictionary. Our approach draws inspiration from conventional dictionary learning algorithms, enabling effective utilization of signal sparsity. In comparison to several state-of-the-art methods, our method achieves superior reconstruction quality and demonstrates enhanced robustness against noise. The proposed approach is envisioned to offer fresh insights into hyperspectral images reconstruction using deep learning models.