We propose a design of the compact high-resolution photonic crystal (PhC) spectrometer with a wide working bandwidth based on both super-prism and local-super-collimation (LSC) effects. The optimizing methods, finding the ideal incident angle and oblique angle of PhC for a wider working bandwidth and ideal incident beam width and PhC size for a certain resolution requirement, are developed. Besides the theoretical work, for the first time, the experiment of such a PhC spectrometer is conducted in the microwave frequency range, and the beam-splitting effects for different frequencies in a wide working bandwidth agree very well with the theoretical predictions. According to the scalability, with the condition to control the deviations in the fabrication processes the design could be extended to optical frequency ranges, e.g., infrared, visible-light, and ultraviolet ranges. The spectrometer in optical frequencies can be implemented on silicon-on-insulator (SOI) chips as a thin-slab structure so that the operating bandwidth can be expanded further through the multi-layer design. Theoretically, the size of the ultra-high-resolution PhC spectrometer in optical frequency ranges based on our design could be two orders smaller than the traditional design.