In this paper, we present a novel adaptive tap algorithm for partial update adaptive filters used in network echo cancellation. As the channel is typically long and sparse, it is unnecessary and inefficient to update all of the taps. Although partial update algorithms can be used to solve this problem, it is difficult to predetermine a fixed number of partial-update taps without a priori knowledge of the channel. We propose a partial update strategy which adapts not only the filter coefficients but also the number of taps to be updated. A novel adaptive tap partial update algorithm, Sparseness-Controlled Adaptive Tap IPNLMS-MMAX (SC-AT IPNLMS-MMAX), is proposed which incorporates a new measure for sparseness. Simulation results show that, compared with the fully updated IPNLMS algorithm, our proposed partial update algorithm has both faster initial convergence and lower computational complexity while achieving almost the same steady-state error.