Multi-view unsupervised feature selection (MUFS) serves as an effective dimensionality reduction technique, garnering extensive attention across various fields. However, existing methods rely on fixed or predefined graphs to represent view similarities, leading to structural bias. Additionally, view-specific discriminative features are often overlooked during consensus learning, undermining the robustness of latent consensus representations. To address these limitations, we introduce a novel MUFS model named Multi-view Unsupervised Feature Selection via Adaptive Graph and Consistency Learning (AGCL). Our approach incorporates a maximum entropy-based adaptive graph learning framework that jointly learns global graph structures and view-specific structural weights, eliminating dependency on fixed similarity metrics. Concurrently, a consistency-constrained label space projection model is designed to explicitly capture both the latent consensus representations and the view-specific representations. An efficient alternating optimization algorithm is developed to solve the resulting objective function. Finally, extensive experiments on nine benchmark datasets demonstrate the superiority of AGCL over state-of-the-art methods in terms of clustering performance.