Colletotrichum species are the most important postharvest spoilage of papaya fruit. The objective of this research was to evaluate the effect of temperature and relative humidity on growth rate and time for growth to become visible of five strains of Colletotrichum gloeosporioides isolated from papaya fruit in a complex medium. As a primary model, the radial growth rates were estimated using the Baranyi and Roberts model in papaya agar. The Solver Excel function was used to obtain the time for visible mycelium (tv). Secondary models obtained with the Rosso’s cardinal model with inflection were applied to describe the effect of temperature on radial growth rate (µ, mm/d). The Arrhenius-Davey model was used to model tv. The obtained models seem to be satisfactory for describing the µ and time tv. The relative humidity (RH) had influence on µ and time tv for all tested C. gloeosporioides isolates, but no model is able to describe the behavior of the fungus. External validation of models on papaya fruit was performed. Growth models were developed with the same models used in vitro. The bias (Bf) and the accuracy factors (Af), as indices for performance evaluation of predictive models in food microbiology, as a function of temperature and RH, were 1.22 and 1.33 for growth rate, and 1.18 and 1.62 for time for visible mycelium respectively indicating good predictions. The supply chain of papaya is complex and require constant conditions and mismatches in can cause damage to fruit. Knowledge of the behavior of C. gloeosporioides on papaya fruit and application of the developed models at the supply chain level will help to establish transport control strategies against these molds. This research has contributed to the first models of growth for C. gloeosporioides in Mexico.