In this paper, the growth of a rising vapour bubble in superheated water was numerically studied using an advanced interface tracking method, called the InterSection Marker (ISM) method. The ISM method is a hybrid Lagrangian-Eulerian Front Tracking algorithm that can model an arbitrary Three-Dimensional (3D) surface within an array of cubic control-volumes. The ISM method has cell-by-cell remeshing capability that is volume conservative, maintains surface continuity and is suited for tracking interface deformation in multiphase flow simulations. This method was previously used in adiabatic bubble rise simulation with no heat and mass transfers to or from the bubble were considered. This present work will extend the ISM method's application to simulate vapour bubble growth in superheated water with the inclusion of additional physics, such as the convective heat transfer mechanism and the phase change. Coupled with an in-house variable-density and variable-viscosity single-fluid flow solver, the method was used to simulate vapour bubble growth due to the convective action. The forces such as the surface tension and the buoyancy were included in the momentum equation. The source terms for the mass transfer were also modelled in the CFD governing equations to simulate the growth. Bubble properties such as size, shape, velocity, drag coefficient, and convective heat transfer coefficient were predicted. Effects of surface tension and temperature on the bubble characteristic were also discussed. Obtained numerical results were compared against the analytical and past works and found to be in good agreement.