In real-time embedded systems, there is requirement for adapting both energy consumption and Quality of Services (QoS) of tasks according to their importance. This paper proposes an adaptive power-aware resource allocation method to resolve a trade-off between the energy consumption and QoS levels according to their importance with guaranteeing fairness. The proposed resource allocator consists of two components: the total resource optimizer to search for the optimal total resource and QoS-fairness-based allocator to allocate resource to tasks guaranteeing the fairness. These components adaptively achieve the optimal resource allocation formulated by a nonlinear optimization problem with the time complexity O(n) for the number of tasks n even if tasks' characteristics cannot be identified precisely. The simulation result shows that the rapidness of the convergence of the resource allocation to the optimal one is suitable for real-time systems with large number of tasks.