Time-varying complex-valued tensor inverse (TVCTI) is a public problem worthy of being studied, while numerical solutions for the TVCTI are not effective enough. This work aims to find the accurate solution to the TVCTI using zeroing neural network (ZNN), which is an effective tool in terms of solving time-varying problems and is improved in this article to solve the TVCTI problem for the first time. Based on the design idea of ZNN, an error-adaptive dynamic parameter and a new enhanced segmented signum exponential activation function (ESS-EAF) are first designed and applied to the ZNN. Then a dynamic-varying parameter-enhanced ZNN (DVPEZNN) model is proposed to solve the TVCTI problem. The convergence and robustness of the DVPEZNN model are theoretically analyzed and discussed. In order to highlight better convergence and robustness of the DVPEZNN model, it is compared with four varying-parameter ZNN models in the illustrative example. The results show that the DVPEZNN model has better convergence and robustness than the other four ZNN models in different situations. In addition, the state solution sequence generated by the DVPEZNN model in the process of solving the TVCTI cooperates with the chaotic system and deoxyribonucleic acid (DNA) coding rules to obtain the chaotic-ZNN-DNA (CZD) image encryption algorithm, which can encrypt and decrypt images with good performance.