3C-SiC has been heteroepitaxially grown by low-pressure chemical vapor deposition (CVD) on the molecular beam epitaxy (MBE) 3C-SiC layer which has been grown on miscut Si(001) substrates inclined in the [110] direction. The reflection high-energy electron diffraction (RHEED) patterns obtained from the 3C-SiC film grown by CVD directly on the miscut Si(001)-4 degrees[110] substrate without MBE layers show 3 x 2 + 90 degrees-rotated 2 x 3 structure which provides evidence of the existence of anti-phase boundaries. However, the RHEED patterns obtained from the 3C-SiC film grown by CVD on the surface-structure-controlled MBE layer on the miscut Si(001)-4 degrees[110] substrate show single-phase 3x2 structure. Surface morphology of 3C-SiC(001) grown by CVD on the MBE layer is dependent on the miscut direction of the Si substrates. The preferential [1(1) over bar 0] growth direction on 3C-SiC(001) plays an important role in forming the single-phase growth and the surface morphologies. The 3C-SiC films grown by CVD/MBE exhibit little strain, while the 3C-SiC film grown by CVD exhibits tensile strain.