This paper studies the proactive eavesdropping for the potential energy-constrained suspicious communication system with one full-duplex-enabled legitimate monitor. Specifically, for such a system, we consider the proactive eavesdropping over finite time blocks under the off-line framework. In each time block, the monitor first acts as the masked power beacon deliberately to proceed wireless energy transfer to the suspicious transmitter for its uplink data transmission, then adaptively executes jamming, passive eavesdropping or assisting strategy based on our provided exact channel condition with strict proofs. According to these adaptive strategies and considering the optimization of transmit power at the monitor, we aim to solve the problem of sum eavesdropping rates maximization over N (N ≥ 1) time blocks subject to limited power at the monitor, which is explained as a difficult mixed-inter nonlinear programming (MINLP) problem. Fortunately, it is shown that this MINLP problem can be divided into one jamming subproblem and one passive eavesdropping/assisting subproblem. To observe the achieve performance bound, we firstly exploit the exhaustive search based algorithm and block coordinate descent (BCD) based algorithm to solve these two subproblems, respectively. In addition, in order to decrease the time complexities, we further propose one jamming power efficiency sorting based heuristic algorithm and one signal-to-noise ratio (SNR) approximation based fast algorithm. Numerical results present the considerable gains brought from our proposed adaptive proactive eavesdropping strategy.INDEX TERMS Energy-constrained system, jamming, passive eavesdropping, assisting, sum eavesdropping rates maximization.