Contemporary computer systems exploits DVFS (Dynamic Voltage/Frequency Scaling) technology for balancing performance and power consumption. The efficiency of DVFS depends on how much performance we get for larger power consumption due to elevated CPU frequency. Especially for memory-bounded applications, higher CPU frequency often does not result in higher performance. In this paper, we present an upper bound of CPU frequency scaling based on memory accesses. It is observed that the performance gain due to higher CPU frequency is limited by memory accesses (last level cache misses) per instructions by experiments. Using the results, we present the CPU frequency upper bound with little performance gain. Experimental results show that for a memory-bounded application, applying the frequency upper bound enhances the energy efficiency of the application by above 30%.