Using the advanced algorithm combining parallel computing, adaptive mesh re-griding and multigrid methods, quantitative 3D phase-field simulations of non-isothermal solidification of binary alloy were carried out. The 3D phase-field simulation results were compared with the analytical LKT (Lipton, Kurz and Trivedi) theory. For comparison, the simulation and analytical results for 2D cases were also given. The 3D phase-field simulation results support the transport portion of the LKT theory. However, the tip radius and tip velocity predicted by the simulations are not in good agreement with the LKT theory over the whole range of undercooling. The stability parameter calculated from phase-field simulations varies significantly with the Peclet number, indicating that the stability criterion, which assumes that the stability parameter is constant, is invalid.