This paper deals with active noise control (ANC) for impulsive noise sources being modeled using non-Gaussian stable process. The filtered-x-LMS (FxLMS) 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 (FxLMP) algorithm - based on minimizing the fractional lower order moment (FLOM) - gives robust performance for impulsive ANC; however, its convergence speed is very slow. This paper proposes modifying and employing a generalized normalized LMP (GNLMP) algorithm for impulsive ANC. The proposed approach is based on data-reusing (DR) type adaptive algorithm. The main idea is to improve the stability by efficiently normalizing the step-size, and improve the convergence speed by reusing the recent data. Extensive simulations are carried out, which demonstrate the effectiveness of the proposed algorithm in comparison with the existing algorithms.