A wide-band, high-resolution vacuum semi-von Hamos spectrometer has been developed for analyzing the X-rays spectra of K-shell multi-ionization atoms. The spectrometer covers an energy dynamic range of 0.6 to 18 keV with a corresponding single exposure spectral bandwidth of 0.25–1.2 keV. This capability is achieved by the combination of different cylindrically bent crystals and an X-ray CCD detector mounted on a twistable bellows, allowing modulation of the Bragg angles from 27° to 47°. A detailed mathematical description is employed to understand the dependence of the geometrical parameters of the spectrometer on the imaging properties, energy spectrum bandwidth, resolving power, solid angle, and other relevant spectrometer characteristics. An energy calibration has been performed by using K X-rays generated by 10–30 keV electron beam interactions with solid KCl, CaF2 and Se targets. The spectrometer exhibits a resolving power better than 103, enabling the analysis of fine spectral structure of K X-ray transitions and the comparison of X-ray properties between pure elements and their compounds due to chemical effects. The spectrometer also finds applications in various fields requiring precise X-ray measurements, including synchrotron radiation experiments, tokamaks, laser plasma diagnostics and laboratory astrophysics.