We investigate the problem of resource allocation in a downlink orthogonal frequency-division multiple access (OFDMA) broadband network with an eavesdropper under the condition that both legitimate users and the eavesdropper are with imperfect channel state information (CSI). We consider three kinds of imperfect CSI: (1) noise and channel estimation errors, (2) feedback delay and channel prediction, and (3) limited feedback channel capacity, where quantized CSI is studied using rate-distortion theory because it can be used to establish an information-theoretic lower bound on the capacity of the feedback channel. The problem is formulated as joint power and subcarrier allocation to optimize the maximum-minimum (max-min) faess criterion over the users’ secrecy rate. The problem considered is a mixed integer nonlinear programming problem. To reduce the complexity, we propose a two-step suboptimal algorithm that separately performs power and subcarrier allocation. For a given subcarrier assignment, optimal power allocation is achieved by developing an algorithm of polynomial computational complexity. Numerical results show that our proposed algorithm can approximate the optimal solution.