In this paper, a new approach is proposed for designing ultra-low-power FFT (Fast Fourier Transform) system suitable for use in energy harvesting powered sensors. Bit-serial architecture is adopted to reduce the power consumption of butterfly operation. Simulation results show that, compared with state-of-the-art bit-serial and conventional parallel processors, the proposed technique is superior in terms of silicon area, power consumption, dynamic energy use due to variable precision arithmetic. A sample design of a 64-point FFT shows that the implementation can save about 40% area and 36% leakage power compared with a conventional parallel counterpart, accordingly achieving significant power benefits at a low sample rate and low voltage domain. The dynamic variation of the arithmetic precision can be achieved through a simple modification of the controller with hardware area overhead of 10% gate count.