Device-free localization (DFL), which does not require any devices to be attached to target(s), has become an appealing technology for many applications, such as intrusion detection and elderly monitoring. To achieve high localization accuracy, most recent DFL methods rely on collecting a large number of received signal strength (RSS) changes distorted by target(s). Consequently, the incurred high energy consumption renders them infeasible for resource-constraint networks, such as wireless sensor networks. This paper introduces an energy-efficient framework for high-precision multi-target-adaptive device-free localization (E-HIPA). Compared with the existing methods, E-HIPA demands fewer transceivers, applies the compressive sensing (CS) theory to guarantee high localization accuracy with less RSS change measurements. The motivation behind the proposed E-HIPA is the sparse nature of multi-target locations in the spatial domain. Before taking advantage of this intrinsic sparseness, we theoretically prove the validity of the proposed CS-based framework problem formulation. Based on the formulation, the proposed E-HIPA primarily includes an adaptive orthogonal matching pursuit (AOMP) algorithm, by which it is capable of recovering the precise location vector with high probability, even for a more practical scenario with unknown target number. Experimental results via real testbed demonstrate that, compared with the previous state-of-the-art solutions, i.e., RTI, SCPL, and RASS approaches, E-HIPA reduces the energy consumption by up to 69 percent with meter-level localization accuracy.