In inertial confined fusion experiments, an excellent-performance and high-efficiency X-ray source plays an important role in X-ray radiography schemes. Indeed, it can be used in a variety of X-ray experimental techniques. The mono-chromaticity, flux intensity, degree of collimation (the radiation can be transported long distances without loss), and spot size of the X-ray source affect the quality of imaging. Ray-tracing simulations, which are validated by experimental results, demonstrate that high-intensity collimated X-ray beams can be produced from an isotropic X-ray source. Therefore, a method of improving the performance of an X-ray source from a laser-produced plasma is presented. A spherically bent crystal is used to collimate mono-chromatic X-rays emitted from a laser-produced plasma. Here we design a spherically bent crystal spectrometer system for collimating the laser-produced X-rays. The system performance is experimentally tested at the Shenguang Ⅱ (SGⅡ) laser facility located in Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences. The beam divergence is measured by using a metal grid placed downstream from the crystal, the metal grid that possesses wires with 60 μm in diameter and 127 μm in period. An imaging plate (IP) is placed at various distances downstream from grid. The quality of the generated beam is monitored by measuring the dimensions of the grid image formed by the beam on IP. While the narrow range of wavelength is measured with a spherically bent crystal spectrometer. Experimental results show that the spherically bent crystal spectrometer system can produce quasi-monochromatic (10^-3 < △ λ/λ <10^-2) X-ray beams with a high degree of collimation (less than 2 mrad divergence), uniform spot size (~500 μm), and a relative tenability in the wide spectral range. The influences of various experimental parameters on the quality of beam collimation are evaluated in two ways. They can be investigated in test experiments by representing the beam divergence distribution as a function of Bragg angle. In another study of the effect of the aberrations, when the incident beam on the spherically bent crystal is not normal, the beam is less collimated in the tangential plane, and out of collimation in the sagittal plane. Following the ray-tracing method, we analyze the diffracted beam divergence produced by the astigmatic aberration. The qualitative conclusion is that the good agreement with the experimental results is obtained. By fully utilizing limited Bragg angle range, the spherically bent crystal spectrometer system can realize collimated diffracted X-ray beams with divergence of less than 1 mrad by using a laser-produced plasma X-ray source under the appropriately experimental parameters.