Keyword-spotting (KWS) plays a crucial role in human machine interactions involving smart devices. And in most of the KWS systems, Mel Frequency Cepstral Coefficients (MFCC) acts as the feature extractor and consumes an unneglectable amount of computational load and resource. In this paper, to reach a trade-off between accuracy and power consumption, we proposed a modified MFCC algorithm, the computational load of which can be reduced by 82% for multiplications and 66% for additions. Using the Google Speech Command Dataset (GSCD), 96.09% accuracy is achieved for ten keywords. Then, following a hardware/algorithm co-optimized approach, we design an energy efficient hardware architecture for MFCC. Implemented in SMIC 65nm process, our circuit achieves a power consumption of $2.81 \mu\mathrm{W}$ while operating at 1.0V supply voltage with 16kHz clock, which is 4.5x less than the related work that under the same process technology.