To make use of the sparsity property of broadband multipath wireless communication channels, we mathematically propose an l p -norm-constrained proportionate normalized least-mean-square (LP-PNLMS) sparse channel estimation algorithm. A general l p -norm is weighted by the gain matrix and is incorporated into the cost function of the proportionate normalized least-mean-square (PNLMS) algorithm. This integration is equivalent to adding a zero attractor to the iterations, by which the convergence speed and steady-state performance of the inactive taps are significantly improved. Our simulation results demonstrate that the proposed algorithm can effectively improve the estimation performance of the PNLMS-based algorithm for sparse channel estimation applications.