Constraint solving is a fundamental approach for verifying deep neural network (DNN). In the field of AI safety, DNNs often undergo modifications in their structure and parameters for purposes such as repair or attack. In such scenarios, the problem of incremental DNN verification is proposed, which aims to determine whether a safety property still holds after the DNN has been modified. To address this, an incremental satisfiability modulo theory (SMT) algorithm based on the Reluplex framework is presented. The proposed algorithm, DeepInc, leverages the key features of the configurations from the previous solving procedure, heuristically checking whether these features can be applied to prove the correctness of the modified DNN. Experimental results demonstrate that DeepInc outperforms Marabou in terms of efficiency in most cases. Moreover, for cases where the safety property is violated both before and after modification, DeepInc achieves significantly faster performance, even when compared to the state-of-the-art verifier α, β-CROWN.