Optical MEMS is a challenging new field that combines micro- optics with micro-mechanics in order to build compact systems. In this paper we present a miniaturized Fourier transform spectrometer (FTS) fabricated on silicon. The FTS is a Michelson interferometer with one scanning mirror. The motion of the mirror is carried out by a new type of electrostatic comb drive actuator. The mirror is designed to be linear with respect to the applied voltage. Experimentally, we have measured a mirror displacement of 38.5 micrometer corresponding to a maximum optical path difference of 77 micrometer. The applied voltage was plus or minus 10 V and the non-linearity of the driving system is plus or minus 0.25 micrometer. A method is presented to correct the spectrum in order to get rid of the non-linearity. The measured resolution of the spectrometer after the phase correction is 16 nm at a wavelength of 633 nm.