Although many years have past from the pioneer work of Lord Rayleigh [1] on bubble growth in the inertia controlled regime and later from Scriven [2], Plesset and Zwick [3] for the diffusion controlled regime, we are still missing mathematical model able to predict accurately both situations. Advances in computational power open the possibility of exploring up-close the transport phenomena in the vicinity of the liquid-vapor interface at an unprecedented resolution. Nonetheless, a high numerical resolution is not enough to fully solve the general problem of bubble growth. New models based on a sharp-interface interpretation of the liquid-vapor interface, have proven to provide accurate results in the diffusion controlled regime, however, these models must assume the interface temperature at the saturation value, restricting their application to physical situations where the evaporation rate satisfies the Stefan condition and bubbles are big enough as to neglect the curvature effects in the interface temperature. In an attempt to provide a more general framework to study bubble growth, a new phase-field model has recently been derived, where no assumption is made on the interface temperature. In this new model, the evaporation rate depends on the local interface temperature and not directly on the heat balance at the liquid-vapor interface. In principle, this particular feature of the model should allow us to simulate both, the inertia and diffusion controlled regimes, but the model has only been validated for the latter. The next step in the validation process is the simulation of bubble growth under convective conditions. Experiments of single bubbles growing and rising up under normal gravity conditions have shown that the growth exponent is about 0.8, in contrast to the value of 1.0 for the inertial controlled regime and 0.5 for the diffusion controlled regime. In this work, fully three dimensional phase-field simulations of bubble growth under convective conditions are presented, where the predicted bubble size and growth exponent compare very well to experimental observations.