A high-resolution extreme ultraviolet (EUV) spectrometer has been developed to diagnose the magnetically confined plasmas. A holographic spherical varied line spacing concave grating which provides a flat focal plane is used as the diffraction element working with the grazing incidence angle of 3°. The nominal groove density is 1 200 lines·mm-1. A deeply cooled back-illuminated CCD camera is used as the spectra detector and a mechanical shutter is used to control the time of exposure. It covers the wavelength range of 5~50 nm with the CCD cameral moving along the spectra focal plane to cover different wavelength range interested. Spectrometer design is presented and it was tested by a Penning discharge light source. By the wavelength calibration, the actual parameters of the optical system were calculated and the wavelength accuracy is 0.003 nm. Results show that the spectral resolution is about 0.015 nm at 20 nm with the width of entrance slit opened at 30 μm, which agrees with the design goal.