Extremely large-scale massive MIMO (XL-MIMO) has been reviewed as a promising technology for future wireless communications. The deployment of XL-MIMO, especially at high-frequency bands, leads to users being located in the near-field region instead of the conventional far-field. This letter proposes efficient model-based deep learning algorithms for estimating the near-field wireless channel of XL-MIMO communications. In particular, we first formulate the XL-MIMO near-field channel estimation task as a compressed sensing problem using the spatial gridding-based sparsifying dictionary, and then solve the resulting problem by applying the Learning Iterative Shrinkage and Thresholding Algorithm (LISTA). Due to the near-field characteristic, the spatial gridding-based sparsifying dictionary may result in low channel estimation accuracy and a heavy computational burden. To address this issue, we further propose a new sparsifying dictionary learning-LISTA (SDL-LISTA) algorithm that formulates the sparsifying dictionary as a neural network layer and embeds it into LISTA neural network. The numerical results show that our proposed algorithms outperform non-learning benchmark schemes, and SDL-LISTA achieves better performance than LISTA with ten times atoms reduction.