Incomplete multi-view data classification poses significant challenges due to the common issue of missing views in real-world scenarios. Despite advancements, existing methods often fail to provide reliable predictions, largely due to the uncertainty of missing views and the inconsistent quality of imputed data. To tackle these problems, we propose a novel framework called Evidential Deep Partial Multi-View Classification (EDP-MVC). Initially, we use K-means imputation to address missing views, creating a complete set of multi-view data. However, the potential conflicts and uncertainties within this imputed data can affect the reliability of downstream inferences. To manage this, we introduce a Conflict-Aware Evidential Fusion Network (CAEFN), which dynamically adjusts based on the reliability of the evidence, ensuring trustworthy discount fusion and producing reliable inference outcomes. Comprehensive experiments on various benchmark datasets reveal EDP-MVC not only matches but often surpasses the performance of state-of-the-art methods.