In this work, we investigate a wireless powered communication network (WPCN) where multiple eavesdroppers attempt to intercept the information between a hybrid access-point (H-AP) and an energy harvesting (EH) user. During the first energy transfer (ET) phase, the EH user and an EH cooperative jammer harvest energy from the transmitted signals of the H- AP. Then, in the next information transfer (IT) phase, the user sends confidential information to the H-AP while the jammer broadcasts artificial noises to the eavesdroppers by utilizing their previously harvested energy. We particularly consider optimization of the time allocation between the ET and the IT phases by which the secrecy rate is maximized. To cut down a computational burden, a low-complexity closed-form solution of the time allocation factor with some interesting behaviors will be proposed by a worst-case approximation. Through simulation results, we evaluate the performance of our proposed scheme and show that a performance gain compared to conventional schemes becomes clearer with the increased number of eavesdroppers.