Energy Harvesting (EH) technology enables Device-to-Device (D2D) User Equipments (DUEs) to harvest energy from ambient energy, making contributions to green communications and breaking the single battery-powered and the regional limitations of device deployment. The joint problem of energy harvesting and resource allocation in EH-based D2D Communication Networks (EH-DCNs) is a challenge issue. In this paper, we investigate the joint problem of resource allocation and EH time slot allocation of DUEs in EH-DCNs, where the DUEs harvest energy and multiplex Cellular User Equipments (CUEs) uplink resources. A channel assignment, power allocation and EH time slot allocation problem in EH-DCNs is formulated. The goal is to maximize energy-and spectral-efficiency with α-fairness while guaranteeing the EH constraints of DUEs and the quality of service of CUEs. The formulated problem is a non-convex mixed integer multi-objective optimization problem. In order to solve the formulated problem, the multi-objective optimization problem is transformed into a single-objective optimization problem based on the weight sum method. We propose a joint iterative algorithm based on Lagrangian dual decomposition for α > 0 and α = 0, respectively. Numerical results illustrate that the proposed algorithm achieves higher energy efficiency and spectral efficiency for different network parameter settings.