Augmented Reality (AR) applications are becoming more and more popular, and smart devices are the most common platform for running AR applications, such as online games, travel guides, and personal assistants. However, these types of AR applications are usually interactive applications that require fast response time and an extremely high power consumption. AR applications need to be supported by highly adaptable multi-core processors equipped smart devices where the optimal low-power control technique, should be used. In this paper, the power consumption model of AR application workloads are mathematically modeled, taking into account the dynamic voltage and frequency scaling (DVFS) of the multi-core central processing unit (CPU) and the parallel execution of multi-core CPUs. Based on the proposed model, the optimal core operation frequency and minimized power consumption are derived. Experimental results show that the proposed scheme satisfies the interaction time limit with the lowest energy consumption.