Composite system reliability (CSR) evaluations suffer from heavy computational burdens because an enormous number of sampled system states must be analyzed. Recently, data-driven approaches are of growing interest because they can accelerate such evaluations by preidentifying success/failure samples. However, the current approaches are limited by unsatisfactory accuracy. Essentially, the main reason is that the data-driven results are not credible. In this article, a trustable data-driven framework based on a deep neural network (DNN) is proposed to enable accurate and credible results for CSR evaluations by the following two aspects: First, a fine-grained identification method with an effective learning strategy is proposed to effectively extract the data features of CSR evaluations and improve the identification accuracy of failure samples. Second, a secure strategy including adaptability criteria and a correction method for the DNN is proposed to guarantee the accuracy of data-driven results. The strategy can determine whether the DNN is utilized to evaluate CSR and reasonably correct the DNN outputs. The simulation results demonstrate the effectiveness of the proposed methods.