Neural networks in safety-critical applications face increasing safety and security concerns due to their susceptibility to little disturbance. In this paper, we propose DeepCDCL, a novel neural network verification framework based on the Conflict-Driven Clause Learning (CDCL) algorithm. We introduce an asynchronous clause learning and management structure, reducing redundant time consumption compared to the direct application of the CDCL framework. Furthermore, we also provide a detailed evaluation of the performance of our approach on the ACAS Xu and MNIST datasets, showing that a significant speed-up is achieved in most cases.