We propose a modified version of frequency domain least mean square algorithm, or, fast least mean square (FLMS) algorithm that achieves better convergence in frequency domain with a marginal increment in implementation Complexity than the former one. The proposed algorithm, leaky FLMS (LFLMS), mainly differs from FLMS by virtue of a leaky factor which is dependent on the algorithm step size parameter and improves the convergence behaviour. We apply the proposed algorithm in case of an adaptive channel equalizer. The performance of the proposed algorithm is examined in the said application with respect to the mean square error (MSE) performance as well as bit error rate (BER) versus signal to noise ratio (SNR) curves.