We present a new design for the fabrication of concave gratings with large grating constants for flat-field miniature spectrometers with a wide spectral band. In this new design, one of the two optical paths for the holographic lithography of a curved grating structure with variable line spacing is modified by adding a concave lens in front of the point source. The addition of the concave lens allows the real point source, as well as the spatial filter for generating this point source, to be moved back. In this manner, the two spatial filters for generating two point sources are separated. Avoiding the physical conflict between these two spatial filters reduces the difficulty of fabricating large-constant concave gratings. Experimental results verify the feasibility of the proposed design in fabricating concave gratings with large grating constants. The resolution of a spectrometer using the fabricated concave grating is evaluated and found to be better than 1.1 nm across a spectral band ranging from 360 nm to 825 nm.