In this paper, the application of Non-Orthogonal Multiple Access (NOMA) is investigated in a multiple-input single-output network consisting of multiple legitimate users and a potential eavesdropper. To support secure transmissions from legitimate users, two NOMA Secrecy Sum Rate Transmit BeamForming (NOMA-SSR-TBF) schemes are proposed to maximise the SSR of a Base Station (BS) with sufficient and insufficient transmit power. For BS with sufficient transmit power, an artificial jamming beamforming design scheme is proposed to disrupt the potential eavesdropping without impacting the legitimate transmissions. In addition, for BS with insufficient transmit power, a modified successive interference cancellation decoding sequence is used to reduce the impact of artificial jamming on legitimate transmissions. More specifically, iterative algorithm for the successive convex approximation are provided to jointly optimise the vectors of transmit beamforming and artificial jamming. Experimental results demonstrate that the proposed NOMA-SSR-TBF schemes outperforms the existing works, such as the maximized artificial jamming power scheme, the maximized artificial jamming power scheme with artificial jamming beamforming design and maximized secrecy sum rate scheme without artificial jamming beamforming design.