As an important optical splitting element, grating is used in many different spectrometers and spectrographs. Spherical varied-line-spacing grating (SVLSG) is easily combined with array detectors to get a wide wavelength range of spectrums in one time, because it can focus the spectrums in approximately a plane. Therefore, it’s widely used in many spectral instruments. We usually only know the central groove density of a commercial grating and its mounting parameters, while its line spacing parameters are unknown. Moreover, the mounting parameters are optimized within the whole using wavelength range of the grating. However, in most circumstances only part of the wavelength range is used. Therefore, the mounting parameters are not optimized for the needed wavelength range. Under this condition, in this article we developed a method based on the focusing theory of the flat-field grating and the mounting parameters the manufacture provided to deduce the line spacing parameters of the grating. With these parameters, we can optimize the detector position according to the wavelength range we need and ray tracing can be done to test the optical system. In this article we developed a high spectral resolution ultraviolet spectrograph, covering a wavelength range of 230~280 nm. The grating used in this spectrograph has a central groove density of 1 200 lines·mm-1 and a designed wavelength range of 170~500 nm. We deduced the line spacing parameters of the grating and optimized the detector mounting parameters. Hollow cathode lamps of different elements were used to calibrate the spectrograph and test the spectral resolution of it. Wavelength calibration of the spectrograph has been done with the parameter fitting method, and the calibration accuracy is better than 0.01 nm. Results show the spectral resolution of the spectral graph is about 0.08 nm at 280.20 nm.