A modified version of proportionate normalized least mean square (PNLMS) algorithm that achieves faster convergence in time domain with a marginal increment in implementation complexity than the existing one is proposed. The proposed algorithm, leaky PNLMS (LPNLMS), mainly differs from PNLMS by virtue of a leaky factor which is dependent on the algorithm step size parameter and speeds up the convergence behaviour. We apply the proposed algorithm in case of an adaptive echo canceller. The performance of the proposed algorithm is examined in the said application with respect to the mean square error (MSE) and bit error rate (BER) curves.