At present, an emerging technique called the algorithm unrolling approach has attracted wide attention, because it is capable of developing efficient and interpretable layers to eliminate the black-box nature of deep learning (DL). In this paper, inspired by the sparse unmixing model, we propose a model-driven DL approach, namely, an implicit variable iterative unrolling network (IVIU-Net). First of all, the unmixing performance and adaptive ability of the model are enhanced by introducing learnable parameters into the sparse unmixing algorithm. Then, a specific spatial convolution module is integrated into the network to promote the smoothness of the latent abundance map. Finally, a comprehensive loss function with three terms such as average spectral angle distance, HSIs reconstruction error, and spectral information divergence, is presented to train the IVIU-Net in an unsupervised way. Compared to the unmixing results of most existing data-driven DL algorithms, our network has significant advantages in two folds: 1) it is able to achieve better stability instead of relying heavily on the endmember initialization results; 2) it has better interpretability and robustness in the unmixing procedure. Experimental results on synthetic and real data show that the proposed network outperforms the state-of-the-art in terms of better convergence, faster unmixing speed as well as better accuracy.