A new high spectral resolution crystal spectrometer is designed to measure very low emissive X-ray spectra of laser-produced plasma in [EQUATION] nm range. A large open aperture ([EQUATION] (mm)) mica (002) spherically bent crystal with curvature radius [EQUATION] mm is used as dispersive and focusing element. The imaging plate is employed to obtain high spectral resolution with effective area of [EQUATION] (mm). The long designed path of the X-ray spectrometer beam is 980 mm from the source to the detector via the crystal. Experiment is carried out at a 20-J laser facility. X-ray spectra in an absolute intensity scale is obtained from Al laser-produced plasmas created by laser energy of 6.78 J. Samples of spectra obtained with spectral resolution of up to [EQUATION] are presented. The results clearly show that the device is good to diagnose laser high-density plasmas.