In this paper, we argue that a certain kind of discreteness of space-time may imply the existence of gravity as a geometric property of space-time described by general relativity (GR). In particular, the dynamical relationship between matter and space-time holds true not only for macroscopic objects, but also for microscopic particles. This argument provides a possible basis for Einstein’s theory of gravity. Moreover, the Einstein gravitational constant in GR can be determined by the minimum intervals of discrete space-time. Lastly, we note that this new analysis may have some further implications for a complete theory of quantum gravity.