A new normalized least mean square (NLMS)-based identification algorithm is proposed for sparse systems. In the proposed algorithm, a tap-selection matrix is utilized to adaptively locate the nonzero coefficients during the convergence process. The so-called tap-selection matrix is a diagonal matrix consisting of zeros and ones, with ones indicating the locations of the active coefficients. At each iteration, tap weights update based on the product of the tap-selection matrix and previous tap-weight vector in the NLMS style. The tap-selection matrix updates by comparing each tap weight with a pre-determined threshold value. Parameter choice guidelines for the threshold value are provided to facilitate practical use. Steady-state mean square deviation is also analyzed for performance evaluation. Simulation results demonstrate that the proposed NLMS algorithm with tap-selection matrix can effectively locate the nonzero coefficients of the unknown system impulse response, outperforming the existing NLMS-based algorithms for sparse system identifications.