The volume phase holographic (VPH) transmission grating recorded in dichromate gelatin (DCG) with a specific spectral coverage from 420 nm to 760 nm is designed for a novel prism-grating-prism imaging spectrometer. Based on the Rigorous Coupled-Wave Analysis, its performances are predicted and analyzed. The grating is manufactured and its properties are measured experimentally. The diffraction efficiency over the spectral range, the bandwidth, and the angular selectivity of the grating is measured, analyzed and compared with that of the theoretical ones. The results show that by adjusting and controlling the preparation conditions of DCG plates, the exposure time and the post-processing technique of the grating, the VPH transmission grating with high diffraction efficiency approximate to the design requirement can be obtained. The measured peak diffraction efficiency reaches nearly 85% at central wavelength of 590 nm while the average diffraction efficiency is larger than 75% over the required spectral range from 420 nm to 760 nm.