A simplified numerical model is proposed to simulate the crystallization behavior of facet primary crystals of a hypereutectic Al–Si alloy. The alloy is assumed to be solidified in a cooling medium which is at a given temperature, TB. The obtained results are summarized as follows: (1) The average crystal size, d3, decreases as cooling rate, R, increases. When R exceeds a critical level, however, d3 begins to converge to a constant value which depends on TB. (2) The average crystal size depends on the maximum undercooling degree of the liquid phase, ΔTLM. (3) The value of ΔTLM is nearly equal to ΔTm which corresponds to the undercooling degree at the apparent onset of crystallization which is detected from the cooling curve.