A power-aware optimal processor cycle allocation scheme with consideration of fair quality of service (QoS) guarantee in real-time systems is formulated. Although power-aware resource management using dynamic voltage and frequency scaling techniques can be used to resolve the trade-off between QoS maximization and energy consumption minimization, it is also necessary to ensure fair QoS allocation in real-time resource allocation to avoid deterioration of QoS levels. The formulation presented in this paper is a multiple-objective optimization problem in which the objective functions are minimization of total energy consumption and maximization of the QoS level. A Pareto optimal solution representing the trade-off between the two objective functions is obtained numerically using a weighted-sum method for the case that the resource consumption functions are convex. We show an example in case that all resource consumption functions are linear.