The NIRSPEC Brown Dwarf Spectroscopic Survey is a project to obtain a consistent set of high-quality near-IR spectra for each spectral class and sub-class of low-mass and/or sub- stellar objects to provide a new data base for models of the atmosphere of brown dwarfs and extra-solar giant planets. Most of the current targets are L-dwarfs and T-dwarfs discovered by the 2MASS. The survey is begin performed with the recently-commissioned near-IR spectrometer, NIRSPEC, a 1-5 micrometers cryogenic spectrograph at the WM Keck Observatory on Mauna Kea, using resolving powers of R equals 2,500-25,000. Preliminary results for four sources, three L-dwarfs and one T-dwarf, are presented here. Spectra from 1.13-2.33 micrometers at an average resolution of R equals 2,500 illustrate the development of deep steam bands and the weakening of FeH through the L-sequence, and the emergence of methane bands in the T-dwarfs. Complex detail in the spectra are the result of blending of numerous unresolved molecular transitions.