Impulse noise (IN) can seriously degrade the performance of conventional active noise control (ANC) algorithms. Here, we present a novel feedforward ANC algorithm based on an information-theoretic learning framework with the data-reuse scheme of affine-projection-based algorithms. Inspired by the maximum correntropy criterion (MCC), the proposed algorithm is referred to as the modified filtered-x affine-projection-like MCC (MFxAPLMCC). Furthermore, we developed an objective function to maximize the correntropy between the system's desired vectors and the secondary path's output vectors to enhance robustness. Moreover, linear approximation reduces computational complexity, and the optimal step size is derived mathematically to accelerate convergence and increase the noise reduction ratio. The MFxAPLMCC algorithm was thoroughly evaluated in terms of stability and computational complexity; numerical simulations were used to confirm the effectiveness in terms of average noise reduction. The efficiency of our method was verified using three types of input: (1) symmetric alpha-stable (S$\alpha$S) IN, (2) a mixture of sinusoidal and IN, and (3) in-vehicle engine acceleration noise. We also verified the tracking capability of the adaptive algorithm for a case in which the primary path changes abruptly. Furthermore, the real measured acoustic path for ANC in-ear headphone development was used to validate the proposed method in real environments. The proposed algorithm significantly outperformed comparative ANC algorithms in convergence rate and noise reduction ratio. We also confirmed that the theoretical bound for stable step size coincides with the numerical results. The parameter sensitivity of the MFxAPLMCC was analyzed as well.