This paper investigates a secure wireless-powered sensor network (WPSN) with the aid of a cooperative jammer (CJ). A power station (PS) wirelessly charges for a user equipment (UE) and the CJ to securely transmit information to an access point (AP) in the presence of multiple eavesdroppers. Also, the CJ are deployed, which can introduce more interference to degrade the performance of the malicious eavesdroppers. In order to improve the secure performance, we formulate an optimization problem for maximizing the secrecy rate at the AP to jointly design the secure beamformer and the energy time allocation. Since the formulated problem is not convex, we first propose a global optimal solution which employs the semidefinite programming (SDP) relaxation. Also, the tightness of the SDP relaxed solution is evaluated. In addition, we investigate a worst-case scenario, where the energy time allocation is achieved in a closed form. Finally, numerical results are presented to confirm effectiveness of the proposed scheme in comparison to the benchmark scheme. © 2020 Junxia Li et al.