Sensor scheduling for energy-efficient collaborative target tracking in wireless sensor networks (WSNs) is an important problem to deal with the limited network resources. With the recent development and emerging applications of energy acquisition technologies, it has become possible to overcome the bottleneck of battery energy in WSNs using the energy harvesting devices, where theoretically the lifetime of the network could be extended to the infinite. However, the energy harvesting WSN also poses new challenges for sensor scheduling algorithm over the infinite horizon under the limited sensor energy harvesting capabilities. In this article, a novel multistep prediction-based adaptive dynamic programming (MSPADP) approach is proposed for collaborative target tracking in energy harvesting WSNs to schedule sensors over an infinite horizon, according to the ADP mechanism. The “action” module of MSPADP is designed to obtain the sensor scheduling for multiple steps starting from the current step, and implemented by the minimal-cost first search (MCFS) decision tree scheme, and the “critic network” module of MSPADP is iteratively performed to optimize the performance for the remaining infinite steps using neural network. Extended Kalman filter (EKF) is adopted to predict and estimate the target state. The performance index is defined by the tracking accuracy derived from EKF and the energy consumption predicted by the candidate sensor schedule. Theoretical analysis shows the optimality of MSPADP, and simulation results demonstrate its superior tracking performance compared with single-step prediction-based ADP (SSPADP), multistep prediction-based dynamic programming (MSPDP), and multistep prediction-based pruning (MSPP) sensor scheduling approaches. Note to Practitioners-Collaborative target tracking is a typical problem in wireless sensor networks (WSNs) where the sensors need to be scheduled to address the constraints of the limited network resources, such as sensor energy usually supplied by the battery. In the recent years, energy harvesting device has been developed and applied to WSNs to overcome the energy restriction. As the energy harvesting capabilities of the sensors are limited, sensor scheduling remains as a challenging problem and is studied in this article. A novel multistep prediction-based adaptive dynamic programming (MSPADP) approach is proposed for collaborative target tracking, by scheduling sensors for the current time step based on the predictions of the subsequent steps over an infinite horizon. It runs iteratively in two modules: obtaining the previous optimal multistep sensor scheduling and updating the remaining infinite-step performance. Simulation results show its superior tracking performance compared with single-step prediction-based ADP (SSPADP), multistep prediction-based dynamic programming (MSPDP), and multistep prediction-based pruning (MSPP) approaches, and lay a good foundation for the practical applications.