A micromechanical phase-field model is utilized to study the evolution of nano-structure Al3Sc phase in Al-Sc alloy. We study the morphology of Al3Sc precipitates in an Al-Sc alloy by phase-field simulations. Since the precipitates of Al3Sc phase are fully coherent to the Al matrix, the elastic energy will have an influence on the resulting morphology. We have studied numerically the effects of elastic strain energies on shape evolution of Al3Sc phase. The simulated nano-structures evolve from a spherical to cubic shapes. The equilibrium shape of the coherent phase was found to be determined by minimizing the sum of the elastic and interfacial energies through the phase-field equations. A coherency loss is observed when the precipitates reach a specific size. The simulation results show a good agreement with previous experimental studies.