The explosive growth of mobile date traffic and ubiquitous mobile services cause an high energy consumption in mobile devices with limited energy supplies, which has become a bottleneck for deploying device-to-device (D2D) communication. Simultaneous wireless information and power transfer (SWIPT), which enables mobile devices to harvest energy from the radio frequency signals, has emerged as a promising solution to improve the energy efficiency (EE) performance. In this paper, we address joint power control and spectrum resource allocation problem in SWIPT-based energy-harvesting D2D underlay networks. First, we formulate joint optimization problem as a 2-D matching between D2D pairs and cellular user equipments (CUEs), and propose a preference establishment algorithm based on Dinkelbach method and Lagrange dual decomposition. Second, we propose an energy-efficient stable matching algorithm by exploring the Gale-Shapley algorithm, which is able to maximize the EE performance of D2D pairs and the amount of energy harvested by CUEs simultaneously. Third, we provide in-depth theoretical analysis of the proposed matching algorithm in terms of stability, optimality, and complexity. Simulation results demonstrate that the proposed algorithm can bring significant EE performance gains compared with some heuristic algorithms.