In this paper, we investigate a downlink outage- constrained robust resource allocation algorithm for achieving the robust transmission in power-domain non-orthogonal multiple access based underlay cognitive radio networks. Our goal is to maximize the sum energy efficiency of secondary users (SUs) under the consideration of imperfect channel state information, while protecting the data rate requirement of each SU and satisfying the maximum transmission power constraint of the secondary base station as well as the interference temperature constraint of each primary user (PU). The proposed optimization problem is non-convex and difficult to solve. To deal with the intractability of the problem coming from the outage probability constraints, in particular, the closed-form expressions of the outage probabilities of SUs and PUs are derived. The original problem is converted into an equivalent convex problem by using successive convex approximation and parameter transformation. A robust subchannel and power allocation algorithm is developed to solve the problem. Simulation results show the effectiveness of the proposed algorithm by comparing with the existing algorithms.