A delay-aware resource allocation algorithm for the heterogeneous multi-radio access (MRA) system, where multiple mobile terminals are served by long term evolution (LTE) and wireless local area network (WLAN) access technologies, is proposed in this paper. Taking both the queue dynamics and physical layer metrics into account when modeling the problem, the algorithm is designed to stabilize all queues while minimizing the total power consumption by minimizing the upper bound of the drift-plus-penalty expression based on Lyapunov optimization theory. Dividing the primary mixed integer programming problem into two sub-problems, the close-form suboptimal solution can be obtained through the standard techniques of the convex minimization with relatively low complexity. The simulation results show that a fundamental improvement in terms of delay performance can be achieved by the proposed algorithm compared with the conventional algorithm based on the sum-rate maximization.