Side-channel attacks (SCAs) are powerful noninvasive attacks that can be used for leaking the secret key of integrated circuits (ICs). Numerous countermeasures were proposed to elevate the security level of ICs against SCAs. Unfortunately, it is quite inconvenient to predict the security levels of these countermeasures since no solid mathematical model exists in the literature. In this paper, neural network (NN)-based entropy is proposed to model the resilience of a system against SCAs. The NN-based entropy model well links the side-channel leakages and probabilities with the neurons and weights of NNs, respectively. In such a circumstance, the NN-based entropy can be used for modeling the robustness of countermeasures since a one-to-one relationship is established between the NN-based entropy and the measurement-to-disclose (MTD) enhancement ratio related with the countermeasures. As demonstrated in the result, the proposed NN-based entropy metric shows 100% consistency with the MTD enhancement ratio if multiple SCA countermeasures are employed into a system.