This study proposes and demonstrates a simple method for improving the energy resolution in a single-shot X-ray spectrometer, which consists of a focusing mirror and a single-crystal analyzer. Two Si(220) channel-cut crystals arranged in a non-dispersive geometry are employed as the analyzer. The angular width of diffraction for the multi-crystal analyzer is reduced by detuning one of the crystals, thereby enhancing the energy resolution of the spectrometer while maintaining the energy range. A proof-of-principle experiment with 10.4 keV X-rays clearly shows a resolution enhancement by a factor of two. It was found that X-ray penetration within the crystals broadened the point-spread function on the detector, significantly impacting the energy resolution under highly detuned conditions. A long detector distance of greater than 14 m is expected to achieve a high energy resolution of 100 meV and a range of 80 eV, enabling full spectral characterization of X-ray free-electron laser radiation as well as advanced spectroscopy techniques.