Nonlinear active noise control (NANC) systems employing Volterra filter suffer from the stability issues in the presence of impulsive noise. To solve this problem, we combine the second-order Volterra (SOV) filter and maximum correntropy criterion (MCC) in this paper. The Volterra filter-x maximum correntropy criterion (VF × MCC) algorithm and Volterra filter-x recursive maximum correntropy (VF × RMC) algorithm are applied to reduce the impulsive noise of NANC. We find that VF × MCC algorithm has a low computational complexity and VF × RMC algorithm converges fast. In order to extract their advantages, we further propose a hybrid algorithm based on the VF × MCC and VF × RMC algorithms. In addition, the normalize step-size version of VF × MCC (VF × nMCC) algorithm is developed to improve the robustness and performance. Meanwhile, we adaptively adjust the kernel size of MCC online based on the sample variance of reference signal to improve the performance of the proposed algorithms. Simulation results in the context of nonlinear active impulsive noise control demonstrate that the proposed algorithms achieve much better performance than the existing algorithms in various noise environments.