Based on the adaptive finite element method， the phase-field model has been employed to simulate the free dendritic growth process governed by capillary anisotropy or kinetic anisotropy. It is illustrated that the free dendritic growth depends sensitively on the degree of the capillary anisotropy or kinetic anisotropy of the solid-liquid interface. As the anisotropies are enhanced， the dendrite tip growth velocity increases， but the dendrite tip radius decreases. These two kinds of anisotropies have different effects on the free dendritic growth behaviors. Under the capillary anisotropic condition， there is a power law relationship between the stability parameter and the capillary anisotropy parameter. And under the kinetic anisotropic condition， there is a linear relationship between the stability parameter and the capillary anisotropy parameter.