Numerical analysis of bubble motion during nucleate boiling is performed by imposing a constant heat flux condition at the base of a heater which occurs in most of boiling experiments. The temporal and spatial variation of a solid surface temperature associated with the bubble growth and departure is investigated by solving a conjugate problem involving conduction in the solid. The vapor-liquid interface is tracked by a level set method which is modified to include the effects of phase change at the interface, contact angle at the wall and evaporative heat flux in a thin liquid micro-layer. Based on the numerical results, the bubble growth pattern and its interaction with the heating solid are discussed. Also, the effect of heating condition on the bubble growth under a micro-gravity condition is investigated.