This paper presents a new cross-layer resource allocation model for multiuser packet-based Orthogonal Frequency Division Multiplexing (OFDM) systems, where the packet arrival process, delay QoS in the application layer and the subcarrier conditions for all users in the physical layer are considered in the MAC layer design. The objective of the proposed cross-layer resource allocation is formulated into a constrained optimization problem, which incorporates the three layers into an integrated framework. To solve the problem effectively, we propose an elitist selection adaptive genetic algorithm (ESAGA), in which the probabilities of crossover and mutation are varied depending on the diversity of population. Numerical examples demonstrate the effectiveness of our proposed algorithm. Due to its low computational complexity, our proposed algorithm is very suitable for implementation in a practical system.