In this paper, the process of the free dendritic growth of Mg-0.5 wt.%Al alloy in the basal plane (0001) is simulated in two-dimensional system by using a quantitative phase-field model. A convergence study is carried out to choose the optimal coupling parameter λ and grid width Δx/W0 in simulation. Then we systematically discuss the effects of the anisotropic strength ε and the supersaturation Ω on dendritical tip growth velocity, radius, Péclet number, and stability parameter σ *. Results show that the stability parameter σ * defined by the theory of microscopic solvability is a function of the anisotropy strength ε, i.e., σ* ≅ ε1.81905, which is obviously closest to σ * (ε) ≅ ε 1.75 obtained from the analytical solution. Moreover, for Ω σ * is approximately a constant while it sharply and monotonically decreases with the augment of the value of ε for Ω > 0.6. This indicates that there is a transition from solute-controlled dendrite to kinetic dendrite as Ω increases. Furthermore, the transition of the growth pattern from the snow-like to the circle-like patterns occurs as Ω increases.