A numerical modeling of dissolution and isothermal solidification during the transient liquid-phase (TLP) diffusion bonding process of Al using pure Cu filler metal based on a diffusion-controlled model was carried out. In the modeling, both the changes in volume accompanying interdiffusion between the base metal (Al) and the filler metal (Cu) and the solid-liquid transformation were taken into account by using variable grids. The effect of a load applied to the base metal was also examined by considering simple force balance among the surface and interface energies of the base metal and liquid formed in the bonding region. The early dissolution process simulated by the developed model agreed with the experimental results, and the predicted isothermal solidification time of a sample with an applied load also agreed with the experimental results.