Single crystalline CdTe epitaxial layers (CTELs) are grown on a highly dissimilar (001) SrTiO3 (STO) by molecular beam epitaxy. The optimized growth temperature is determined to be in the range of 210 degrees C-270 degrees C. The crystalline structures of the CTELs are characterized by X-ray diffraction (XRD). The lattice parameters of the CTELs are revealed by the in-plane and out-of-plane reciprocal space mapping, electron microscopy and electron diffraction, and the epitaxial relationships between film and substrate are further summarized as: (111)(cdTe) parallel to (001)(STO), [1-10](cdTe) parallel to [010](STO) and [11-2](CdTe) parallel to [100](STO). The optimized full width at half maximum is yielded to be similar to 108 arcsec. The high crystalline quality and sharp interface are highlighted by the appearance of well-defined fringes of the XRD patterns, electron microscopy and photoluminescence spectra. Finally, the possible growth mechanisms are discussed and compliant epitaxial mechanism can well account for the epitaxial growth of the CdTe(111)/STO(001) epitaxial system. The achievement of the epitaxial growth of the CTELs on (001) STO with atomic flatness and high-crystalline quality will avail to the potential application in photoelectric devices and the further epitaxy of the Hg1-xCdxTe-based infrared detector materials.