ZnO epitaxial layers are grown on (1 1 1)CaF2 substrates by the two-step MBE, in which a 80 nm thick low-temperature buffer layer was predeposited onto CaF2. Structural properties of ZnO layers have been investigated in detail with high-resolution four-crystal diffractometry to get insight into three-dimensional lattice ordering in the epilayers. The results are compared with a ZnO layer grown on CaF2 without a low-temperature buffer layer and reported data of ZnO layers grown on Al2O3. It is found that the low-temperature buffer layer is effective for reducing mosaicity in the layers. The domain size increases and inhomogeneous lattice strain along the growth direction is reduced in ZnO layers grown by two-step MBE. Although the low-temperature buffer layer is effective for improving the in-plane lattice ordering and the ordering along the growth direction, it is more effective for the lattice ordering along the growth direction.