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In this paper, we propose an adaptive sensor scheduling scheme to maximize the network lifetime for energy-constrained wireless sensor networks (WSNs) using adaptive dynamic programming (ADP) method. Based on Kalman filter (KF) prediction, the problem is firstly formulated as an infinite-step constrained maximum optimal control problem with the estimation accuracy constraint at each step. Then, a novel adaptive scheduling scheme based on iterative ADP algorithm is proposed as the solution where the predicted performance index is approximated by a neural network. Analysis of the proposed solution is given which shows that the performance index converges to the optimum. A simulation example is employed to illustrate the applicability of the proposed method.