This paper investigates an outage-constrained secrecy rate maximization (OC-SRM) problem based on the statistical channel uncertainty assumption in an underlay multiple-input multiple-output (MIMO) cognitive radio network, where the secondary transmitter provides simultaneous wireless information and power transfer to receivers. Our objective is to design the transmit covariance matrix and artificial noise aided covariance matrix through maximizing the secrecy rate of the secondary user while satisfying the given outage probability requirements. The designed problem is nonconvex and challenging. We employ the existing theory to reformulate the original problem into two equivalent subproblems by introducing auxiliary variables in order to overcome the difficulty arising from the Shannon capacity expression. The Bernstein-type inequality approach is resorted to conservatively approximate the probabilistic constraints. The merit of the transformation and conversion is that the tractable solutions of the original OC-SRM problem can be easily obtained through solving two convex conic subproblems alternately. Furthermore, we extend the proposed algorithm to solve full uncertainty model design. Numerical results demonstrate the efficacy of the proposed designs.