This paper investigates the secrecy communications of a downlink wireless-powered cooperative non-orthogonal multiple access (NOMA) system with a source node, a relay, a pair of near and far users, and an eavesdropper (Eve). A wireless-powered relay assists the transmission from the source to the far user, and the Eve intends to wiretap the confidential message transmitted to the near user. We propose a dynamic power allocation and friendly jamming based secure transmission scheme. Specifically, the optimal power allocation factors at the source node for the paired NOMA users are obtained to guarantee the perfect successive interference cancellation performance and improve the transmission reliability of the pair of NOMA users. In the direct transmission phase, the source transmits a superimposed signal to the near user and the wireless-powered relay, and the far user serves as a friendly jammer to emit artificial noise to confuse the Eve. In the cooperative transmission phase, the relay utilizes the harvested energy to assist the transmission to the far user. By applying the Gaussian-Chebyshev and Gaussian-Laguerre quadratures, closed-form expressions for the secrecy outage probability of the near user and the connection outage probability of the far user are derived. Simulation results verify the correctness of our theoretical analysis. The superiority of the proposed scheme is also demonstrated for improving the secrecy performance, as compared to the existing cooperative NOMA schemes.