The controlled growth of mono-/double-layer 2H-MoTe2 fully covering the substrate is highly desirable for the future of device fabrication but still remains a challenge. In this study, we present growth of mono-/double-layer 2H-MoTe2 films on graphene terminated 6H-SiC(0 0 0 1) substrates by molecular beam epitaxy (MBE). We develop two distinct processes which achieve better layer-by-layer controllability of stoichiometric films. We further provide a coherent explanation for the Moiré patterns together with the formation of semi-coherent twin boundaries (TBs) in the films and the electronic structure of the films. Our materials are analyzed in detail by reflection high energy electron diffraction (RHEED), X-ray photoemission spectroscopy (XPS), and scanning tunneling microscopy/spectroscopy (STM/STS).