Robust combination synchronization has garnered extensive attention within the domains of science and engineering, particularly in the realm of secure communication in recent years. In contrast to conventional single master-single slave system, the introduction of multiple variables and intricate combination methods in combination synchronization significantly increases the complexity of decryption, boosting the confidentiality and security of signal transmission. However, due to the ubiquity of time-varying external interference, the synchronization results of ordinary methods are not ideal or may even be divergent. In view of these challenges, this paper proposes the integration-enhanced zeroing neural network (IEZNN) model and its associated controller to achieve robust combination synchronization of chaotic systems. Theoretical research fully substantiate the effectiveness of the proposed IEZNN approach and its related controller. Additionally, the numerical findings show that, in comparison to the conventional zeroing neural network (CZNN) method, the controller designed by IEZNN model have remarkable anti-interference performance in the presence of external time-varying disturbances.