A phase-field model for multicomponent alloys based on the binary phase-field model has been developed. The isothermal dendritic growth of Al-Si-Mg alloys is presented as a numerical example, accordingly, the dendrite growing morphology of multicomponent alloys solidification could be simulated realistically using the phase-field model. As the result, the intricate figures such as secondary and tertiary dendrite arms are revealed. The decrease of solute Mg can trigger the growth of the secondary arms and increase the solute microsegregation rate, the tip speed and radius of dendrite. The variation of the speed and the radius in the dendrite tip agrees well with theoretical and experimental results in succinonitrile-acetone system. In addition, the spines of the primary arms have lowest concentration, and the mushy regions between the dendrite secondary arms have the highest concentration; the solute gradients are higher in the vicinity of the S/L interface regions, and highest in the tip.