In real-world scenarios, missing views is common due to the complexity of data collection. Therefore, it is inevitable to classify incomplete multi-view data. Although substantial progress has been achieved, there are still two challenging problems with incomplete multi-view classification: (1) Simply ignoring these missing views is often ineffective, especially under high missing rates, which can lead to incomplete analysis and unreliable results. (2) Most existing multi-view classification models primarily focus on maximizing consistency between different views. However, neglecting specific-view information may lead to decreased performance. To solve the above problems, we propose a novel framework called Trusted Cross-View Completion (TCVC) for incomplete multi-view classification. Specifically, TCVC consists of three modules: Cross-view Feature Learning Module (CVFL), Imputation Module (IM) and Trusted Fusion Module (TFM). First, CVFL mines specific- view information to obtain cross-view reconstruction features. Then, IM restores the missing view by fusing cross-view reconstruction features with weights, guided by uncertainty-aware information. This information is the quality assessment of the cross-view reconstruction features in TFM. Moreover, the recovered views are supervised by cross-view neighborhood-aware. Finally, TFM effectively fuses complete data to generate trusted classification predictions. Extensive experiments show that our method is effective and robust.