Collaborative target tracking is one of the most important applications of wireless sensor networks (WSNs), in which the network must rely on sensor scheduling to balance the tracking accuracy and energy consumption, due to the limited network resources for sensing, communication, and computation. With the recent development of energy acquisition technologies, the building of WSNs based on energy harvesting has become possible to overcome the limitation of battery energy in WSNs, where theoretically the lifetime of the network could be extended to infinite. However, energy-harvesting WSNs pose new technical challenges for collaborative target tracking on how to schedule sensors over the infinite horizon under the restriction on limited sensor energy harvesting capabilities. In this paper, we propose a novel adaptive dynamic programming (ADP)-based multi-sensor scheduling algorithm (ADP-MSS) for collaborative target tracking for energy-harvesting WSNs. ADP-MSS can schedule multiple sensors for each time step over an infinite horizon to achieve high tracking accuracy, based on the extended Kalman filter (EKF) for target state prediction and estimation. Theoretical analysis shows the optimality of ADP-MSS, and simulation results demonstrate its superior tracking accuracy compared with an ADP-based single-sensor scheduling scheme and a simulated-annealing based multi-sensor scheduling scheme.