In this paper, we propose an energy-efficient resource allocation scheme for the downlink of decode-and-forward relay-assisted orthogonal frequency division multiple access systems. The resource allocation is designed based on imperfect channel state information at the transmitter. We jointly optimize the power allocation, data rate allocation, and subcarrier allocation to maximize the system energy efficiency (EE). We formulate the EE problem as a probabilistic mixed non-convex optimization problem, in which the individual power constraints and the outage probability requirements are considered. An iterative algorithm based on bisection method is given to transform the optimization problem into a standard concave form. Also, we consider a proportional fairness design for the EE maximization problem. Simulation results illustrate the effectiveness of the proposed algorithm.