The filtered-x least mean square (FxLMS) algorithm for active noise control (ANC) systems is based on the second order moment of the error signal. In this paper we consider ANC for impulsive noise having peaky distribution with heavy tail. Such impulsive noise can be modeled using non-Gaussian stable process for which the second order moments do not exist, and hence, the FxLMS algorithm becomes unstable. Recently, we have proposed variants of the FxLMS algorithm where an improved performance has been realized by thresholding the input data or by efficiently normalizing the step-size. In this paper, we propose a modified binormalized data-reusing (BNDR) algorithm for impulsive ANC. The proposed algorithm is derived by minimizing a modified cost function, and is based on reusing the past and present samples of data. The computer simulations are carried out to demonstrate the effectiveness of the proposed algorithm. It is shown that an improved performance has been realized with a reasonable increase in computational complexity.