Signaling design for secure transmission in two-user multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) networks with different security requirements is investigated. A base station broadcasts multicast data to all users and unicast data and confidential data targeted to certain users. We categorize the above channel into three communication scenarios depending on the security requirements. The associated problem in each scenario is nonconvex. We propose a unified approach, called the power splitting scheme, for optimizing the rate equations corresponding to each scenario. The proposed method converts the optimization of the secure MIMO-NOMA channel into a set of simpler problems, namely multicast, point-to-point, and wiretap MIMO problems, corresponding to the three basic messages: multicast, private/unicast, and confidential messages. We then leverage existing solutions to design signaling (covariance matrix) for the above problems such that the messages are transmitted with high security and reliability. Numerical results illustrate the efficacy of the proposed covariance matrix (linear precoding and power allocation) design. In the case of no multicast messages, we also reformulate the nonconvex problem into weighted sum rate (WSR) maximization problems by applying the block successive maximization method and generalizing the zero duality gap. The two methods have their advantages and limitations. Power splitting is a general tool that can be applied to the MIMO-NOMA with any combination of the three messages (multicast, private, and confidential) whereas the WSR maximization shows greater potential for secure MIMO-NOMA communication without multicasting. In such cases, the WSR maximization provides a slightly better rate than the power splitting method. © 1991-2012 IEEE.