We develop a high speed spectral domain optical coherence tomography (SD-OCT) system based on a custom-built spectrometer and non-uniform discrete Fourier transform (NDFT) to realize minimized depth dependent sensitivity fall-off. After precise spectral calibration of the spectrometer, NDFT of the acquired spectral data is adopted for image reconstruction. The spectrometer is able to measure a wavelength range of about 138 nm with a spectral resolution of 0.0674 nm at central wavelength of 835 nm, corresponding to an axial imaging range of 2.56 mm in air. Zemax simulations and sensitivity fall-off measurements under two alignment states of the spectrometer are given. Both theoretical simulations and experiments are done to study the depth dependent sensitivity of the developed system based on NDFT in contrast to those based on conventional discrete Fourier transform (DFT) with and without interpolation. In vivo imaging on human finger from volunteer is conducted at A-scan rate of 29 kHz and reconstruction is done based on different methods. The comparing results confirm that reconstruction method based on NDFT indeed improves sensitivity especially at large depth while maintaining the coherence-function-limited depth resolution.