Simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) has attracted extensive attentions due to its prominent advantages to future wireless networks. This correspondence considers a downlink multi-input single-output non-orthogonal multiple access system, in which the STAR-RIS is utilized to improve the secrecy performance. To restrain the internal eavesdropping, we formulate a secrecy rate maximization problem and propose a secure transmission design via the joint active and passive beamforming optimization with optimum power allocation. To decouple optimization variables, the original non-convex problem is divided into two subproblems, which are transformed into convex forms via successive convex approximation and solved by alternating optimization. Simulation results demonstrate the superiority of the proposed scheme in the security enhancement.