This letter deals with active noise control (ANC) for impulsive noise sources being modeled using non-Gaussian stable process. The filtered-x least mean square algorithm is based on minimization of the variance of the error signal and becomes unstable for impulsive noise. The filtered-x least mean p-power algorithm-based on minimizing the fractional lower order moment-gives a robust performance for impulsive ANC; however, its convergence speed is very slow. This letter proposes modifying and employing a generalized normalized LMP algorithm for impulsive ANC. Extensive simulations are carried out which demonstrate the effectiveness of the proposed algorithm.