As an emerging technique, non-orthogonal multiple access (NOMA), which has superior spectral efficiency, is expected to be widely used in future wireless networks. This letter is to study a robust sum rate optimization problem in a NOMA amplify-and-forward (AF) relay network, where the channel uncertainties are modeled by a worst-case model. Our goal is to maximize the worst-case sum rate by jointly designing power allocation and relay beamforming subject to the weak users' quality of service requirements and the transmit power constraint at the relay. The proposed optimization problem is non-convex. To efficiently solve this problem, we employ the cutting-set method, which is an iterative algorithm. In each iterative step, we solve two subproblems, i.e., a joint relay beamforming and power allocation optimization problem for given channels, and a pessimization problem to determine the worst-case channel uncertainties with given relay beamforming and power allocation. Simulation results demonstrate the effectiveness of the proposed robust scheme for NOMA AF relay networks.