In this paper, we propose a novel robust resource allocation algorithm for downlink non-orthogonal multiple access (NOMA) cognitive radio networks with the underlay spectrum sharing mode. To characterize the effect of channel uncertainty, a robust energy efficiency (EE) maximization optimization problem is formulated under the constraints of the maximum interference temperature threshold of primary user, the maximum transmit power of secondary base station, and the outage probability of secondary user’s rate. The non-linear optimization problem is converted into a convex form by using a new parameter transformation. Moreover, the analytical solution of power allocation is obtained by using the Lagrange dual theory. The provided results demonstrate the proposed robust resource allocation scheme can always achieve better EE and outage performance than that of the traditional orthogonal multiple access scheme and the non-robust NOMA scheme.