Phase field modeling has been applied first to simulate microstructural evolution during rapid solidification of small Al-0.02 mole fraction Cu alloy droplets. We use a phase-field model with the parameters determined at a finite interface thickness condition. Numerical computation is stable over a wide temperature range because same interface energy and interface thickness are applied during computation by using temperature dependence of phase field parameters. For numerical efficiency, we adopted rather thick interface thickness, large interface energy and small interface kinetics coefficient, compared with reported values. Nevertheless, overall features of microstructural evolution presented in this study show close resemblance with the reported theoretical predictions and experimental results; initial dendrite/plane-front transition when the nucleation undercooling is small, plane-front/cell and cell/dendrite transition in high interface velocity regime, complete disappearance of dendritic structure in high heat transfer coefficient and deflection phenomena in cellular growth direction.