A velocity spectrometer for a neutral atomic beam has been developed to create a mono-velocity neutral atomic beam. In order to disperse a neutral atomic beam depending on its velocity, a magnetic circuit with a large and uniform magnetic gradient has been developed for the first time. The magnetic circuit was made up of quadrupole field configuration of NdFeB permanent magnets. The magnetic gradient in the circuit was measured to be sufficiently large (1T/cm) and uniform. It is possible to use the magnetic circuit as a focusing lens as well as a prism of the spectrometer for a neutral atomic beam. The resonant fluorescence spectra of the Li atomic beam that passed through the magnetic circuit were measured by using a single mode tunable laser. From the peak shift of the fluorescence spectrum, the exerted force on Li atoms by the magnetic gradient in the circuit was 10000 times as large as the earth's gravity. It is expected that a mono-velocity Li atomic beam of 1000m/s with 1% resolution can be created with a compact experimental arrangement using the developed velocity spectrometer.