A novel concept of on-chip Fourier transform spectrometer is proposed. It consists of semiconductor waveguide directional couplers and NEMS actuators. The optical path difference can be tuned by controlling the NEMS actuators to couple or decouple the directional couplers. With 9 stages of directional couplers, we demonstrate numerically that the spectral resolution can reach up to 4 nm in 1.5 μm to 1.8 μm wavelength range. Further enhancement can be achieved by increasing the number of integrated NEMS driven directional couplers. This design meets the requirement of small size, weight and power and may be useful in future on-chip spectroscopic sensors.