Non-orthogonal multiple access (NOMA) has been recognized as a promising technique for providing high data rates in 5G systems. This letter is to study physical layer security in a single-input single-output (SISO) NOMA system consisting of a transmitter, multiple legitimate users and an eavesdropper. The aim of this letter is to maximize the secrecy sum rate (SSR) of the NOMA system subject to the users’ quality of service (QoS) requirements. We firstly identify the feasible region of the transmit power for satisfying all users’ QoS requirements. Then we derive the closed-form expression of an optimal power allocation policy that maximizes the SSR. Numerical results are provided to show a significant SSR improvement by NOMA compared with conventional orthogonal multiple access (OMA).