Resource-based models of species competition have been introduced recently as an alternative to the classical theory based on the Lotka-Volterra methodological approach to species competition. Considering the resource-based species competition where species growth is restricted by resource availability, simple mathematical models are proposed to investigate the coexistence of two consumers using single finite resources distributed over distinct patches with uneven growth rates. We analyze the equilibrium state and the competing mechanism and make numerical simulation to obtain the following results. (1) By predicting the outcome of species competing for resource by R*, some probabilities do exist. Firstly, species with a lower R* can exclude the one with a higher R*; secondly, species with the same R* or not may expect coexistence; thirdly, species with a higher R* may also exclude the one with a lower R*. The conclusion, however, is not so assured. (2)The between-patch movement enable the more efficient consumer to move to patches with high resource growth rates, which eventually become sources, while low-growth-rate patches effectively become sinks; the source-sink structure facilitates the coexistence of competitive species, while the inferior exploiter allows less migration. (3)At identical population demographic rate, the more different resource growth rate is, the less favorable for species coexistence; while at different population demographic rate, the greater difference of resource growth rate is more likely to facilitate the coexistence. In the nature, species coexistence requires different resource growth rate. (4)Distinct resource growth varies its effect on the stability of competitive species.