In recent years, various deep learning-based methods have been proposed to address the problem of incomplete multi-view clustering. However, these methods still face two major challenges: firstly, due to the incompleteness of views, they are susceptible to noise and irrelevant features, leading to redundant and untargeted learned features; secondly, although these methods attempt to leverage the consistent information across different views for cross-view learning, they often overemphasize consistency, thereby neglecting inter-view differences. To address these issues, this paper proposes a novel method: Sparse-driven Attention with Dual-Consistency Learning Network for Incomplete Multi-view Clustering (SADCL-Net). Specifically, we utilize a sparsity-constrained self-attention module to effectively capture the intrinsic sparsity and local salient information of the data, thereby highlighting key features. Subsequently, we design a Dual-Consistency Learning module, which incorporates a joint entropy term into the consistency loss function to balance the consistency and difference information across views, thereby optimizing the contribution of different views to the final clustering results. Additionally, to avoid potential issues arising from imputing missing data, we integrate feature projection and alignment modules. Our proposed method has been extensively evaluated on four widely-used multi-view datasets, with results prominently demonstrating the significant advantages of SADCL-Net in terms of clustering performance.