Achieving large confidential capacity under the wiretap channel model is a challenge due to the narrow modulation bandwidth and total transmission power constraints. The confidential capacity of a system can be improved through a non-orthogonal multiple access technique that can obtain the highest transmission power in a downlink network. A clustering method is applied to network users who require data with similar contents. Based on the channel gain of each user, cluster heads are selected as agents for the corresponding clusters; then, the total transmission power is shared among the cluster heads. Before the power allocation process, the signal-to-interference-plus-noise ratio of the cluster heads is derived by considering clipping noise to ensure fairness. On this basis, an optimal power allocation scheme is proposed using Lagrangian dual theory. A case is presented to validate the performance of the proposed power allocation scheme. The comparison of the numerical results with those of other schemes shows that the proposed method achieves better performance regarding both secrecy sum capacity and outage probability.