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The dendrite structure of aluminum alloys can be refined with titanium, boron, and rare earth elements. The effect of a refiner on the dendrite sizes was currently neglected in the cellular automata method. The parameter setting of the cellular automata method, considering the effect of rare earth elements on the α-Al dendrite of a hypereutectic AlSi alloy, was systematically investigated. The α-Al primary phase sizes of an AlSi7Cu3Mg alloy with different Y contents are experimentally studiedю With the Y addition of up to 0.2 wt.%, the refinement effect was the most effective, and grain sizes decreased to 0.67 mm. The microstructure simulation by the cellular automata method was studied experimentally and theoretically. By the use of this model, the parameter-setting effect on the Y refinement was more consistent with physical meaning. The calculation results fit the experimental ones well, and the validity and applicability of the model were verified. [ABSTRACT FROM AUTHOR]