Two functions are essential and necessary for the wireless-powered communication network, which are energy beamforming and localization. On one hand, energy beamforming controls the wireless energy waves of the energy access point (E-AP) in order to activate the nodes for transmitting information. On the other hand, locating the nodes is important to network management and location-based services in the wireless power communication network (WPCN). For a large-scale network, cooperative localization that employs neighborhood nodes to participate in positioning unknown target nodes is highly accurate and efficient. However, how to use energy beamforming to achieve highly accurate localization is not fully investigated yet. In this article, we analyze the impacts of energy beamforming on the cooperative localization performance of WPCNs. We formulate the Fisher information matrix (FIM) and the corresponding Cramér-Rao lower bound (CRLB) for the full connected network and a single node, respectively. Then, we propose beamforming schemes to optimize the cooperative localization and the power consumption. For optimal localization problems, we derive the closed-form expression of the optimal energy beamforming. For the optimal energy efficiency problems, we propose semidefinite programming (SDP) solutions to achieve the minimum power consumption while using calibrations to approach the actual localization requirements. Further, we also analyze the impacts of channel uncertainty. Through extensive simulations, the results demonstrate the dominant factors of the localization performance, and the performance improvements of our proposed schemes, which outperform the existing power allocation schemes.