The small-cell technology is promising for spectral-efficiency enhancement. However, it usually requires a huge amount of energy consumption. In this paper, queue state information and channel state information are jointly utilized to minimize the time average of overall energy consumption for a multi-carrier small-cell network, where the inter-cell interference is an intractable problem. Based on the Lyapunov optimization theory, the problem could be solved by dynamically optimizing the problem of user assignment, carrier allocation and power allocation in each time slot. As the optimization problem is NP-hard, we propose a heuristic iteration algorithm to solve it. Numerical results verify that the heuristic algorithm offers an approximate performance as the brute-force algorithm. Moreover, it could bring down the overall energy consumption to different degrees according to the variation of traffic load. Meanwhile, it could achieve the same sum rate as the algorithm which focuses on maximizing system sum rate. The small-cell technology is promising for spectral-efficiency enhancement. However, it usually requires a huge amount of energy consumption. In this paper, queue state information and channel state information are jointly utilized to minimize the time average of overall energy consumption for a Based on the Lyapunov optimization theory, the problem could be solved by dynamically optimizing the problem of user assignment, carrier allocation and power allocation in each time slot. As the optimization problem is NP-hard, we propose a heuristic iteration algorithm to solve it. Numerical results verify that the heuristic algorithm offers an approximate performance as the brute-force algorithm. Moreover, it could bring down the overall energy consumption to different degrees according to the variation of traffic load. Meanwhile, it could achieve the same sum rate as the algorithm which focuses on maximizing system sum rate.