GRUMPY (Galaxy formation with RegUlator Model in PYthon) models the formation of dwarf galaxies. When coupled with realistic mass accretion histories of halos from simulations and reasonable choices for model parameter values, this simple regulator-type framework reproduces a broad range of observed properties of dwarf galaxies over seven orders of magnitude in stellar mass. GRUMPY matches observational constraints on the stellar mass--halo mass relation and observed relations between stellar mass and gas phase and stellar metallicities, gas mass, size, and star formation rate. It also models the general form and diversity of star formation histories (SFHs) of observed dwarf galaxies. The software can be used to predict photometric properties of dwarf galaxies hosted by dark matter haloes in N-body simulations, such as colors, surface brightnesses, and mass-to-light ratios and to forward model observations of dwarf galaxies.