Coded aperture snapshot spectral imager (CASSI) can recover three-dimensional hyperspectral images (HSIs) from two-dimensional compressive measurements. Recently, deep unfolding approaches were shown impressive reconstruction performance among various algorithms. Existing deep unfolding methods usually employ linear projection methods to guide the iterative learning process. However, the linear projections do not include trainable parameters and ignore the essential characteristics of HSI. This paper proposes a novel learning-based deep estimation-enhancement unfolding (DEEU) framework to improve the HSI reconstruction. The deep estimation-enhancement (DEE) module is used to guide the iterative learning process of the network based on the prior information of the CASSI system, and then exploits the intrinsic features of the reconstructed HSI in both spectral and spatial dimensions. In addition, a multi-prior ensemble learning module is proposed to further improve the reconstruction performance without increasing runtime. As with most of deep unfolding methods, we plug a convolutional neural network as a denoiser in each stage of the DEEU framework, which finally forms the proposed DEEU-Net. Comprehensive experiments on both simulation and real datasets demonstrate that the effectiveness of our DEEU framework, and our DEEU-Net can achieve both high reconstruction quality and speed, outperforming the state-of-the-art methods.