In this paper, the growth processes of a single bubble on a fixed single site and the relative heat transfer under different gravity are numerically investigated for saturated water at 0.1MPa. A simplified lubrication theory is used to predict the contribution from the micro-wedge area underneath the growing bubble, while vapor and liquid phases in other macro-area are treated as one fluid by using the continuum interface model. The Level Set Method and constant superficial contact angle are used to capture the interface between the vapor and liquid phases and the motion of contact line on the heating wall, respectively. The numerical results indicate that the equivalent diameter is proportional to about (1/3~1/2)-power of the growing time in spite of whatever gravity levels. But gravity has great influences on both the departure diameter and the growing time. The bubble departure diameter is proportional inversely to about 1/3-power of gravity, while the growing time is proportional inversely to about 4/5-power of gravity. The area-averaged heat fluxes are approximately proportional to the 3/2-power of the wall superheat when the number density of active nucleation sites fixes. Furthermore, this trend has no change with the decrease of gravity.