We have studied the growth of C60 film on GaAs(001) 2×4-β phase surface epitaxially grown by MBE.Due to the delicate equilibrium between the interaction of C60 molecules and the interaction of C60 molecule with the substrate,the toplayer of C60 film,unlike that on the metal and silicon substrate,shows a non-close packed structure.The facet structure of C60 film exhibits that the top-two layers are hcp but the others are fcc,which implies an existence of the phase-transition from hcp to fcc structure in the film growth.The measurement results that the lattice constant of fcc is 1.13 nm,larger of 13% than that of C60 crystal,and hcp is not ideal which is compressed along c-axis.The strain in C60 film and the minimum of the total energy should be responsible for the existence of the phase-transition.On GaAs(001)-c(4×4) surface,the structure of C60 film shows fcc(111) surface and the film grows in three-dimensional mode which is quite different from that on other substrates.