This paper studies the cell-edge user’s performance of a secure multiple-input single-output non-orthogonal multiple-access (MISO-NOMA) system under the Rayleigh fading channel in the presence of an eavesdropper. We suppose a worst-case scenario that an eavesdropper has ideal user detection ability. In particular, we suggest an optimization-based beamforming scheme with MISO-NOMA to improve the security and outage probability of a cell-edge user while maintaining the quality of service of the near-user and degrading the performance of the eavesdropper. To this end, power allocation coefficients are adjusted with the help of target data rates of both the users by utilizing a simultaneous wireless information and power transfer with time switching/power splitting protocol, where the near-user is used to forward the information to cell-edge user. The analytical results demonstrate that our beamformer analysis can achieve reduced outage probability of cell-edge user in the presence of the eavesdropper. Moreover, the provided simulation results validate our theoretical analysis and show that our approach improves the overall performance of a two-user cooperative MISO-NOMA system.