Sensor scheduling is essential to collaborative target tracking in wireless sensor networks (WSNs). In this paper, we present a multi-step adaptive sensor scheduling algorithm (MASS) by selecting the next tasking sensor and its associated sampling interval based on the prediction of tracking accuracy and energy cost over a finite horizon of steps. MASS adopts alternative tracking mode for each prediction step, i.e., the fast tracking mode (FTM) or the tracking maintenance mode (TMM) dependent on whether the estimated or predicted tracking accuracy is satisfactory. The best sensor schedule sequence (BSSS) is found by searching and comparing the candidate sensor schedule sequences (CSSSs) at two levels, i.e., the logical tracking mode level which is simply defined on multi-step tracking modes and the physical quantity performance level by considering the tradeoff between tracking accuracy and energy cost. MASS employs the extended Kalman filter (EKF) algorithm to predict the tracking accuracy and an energy consumption model to predict the energy cost. Simulation results show that, compared with the traditional non-adaptive sensor scheduling algorithm and the single-step adaptive sensor scheduling algorithm, MASS can achieve fast tracking speed and superior energy efficiency without degrading the tracking accuracy