We grow atomically thin molybdenum ditelluride (MoTe2) films on a SiO2/Si substrate by means of metal-organic chemical vapor deposition (MOCVD). Our Raman spectroscopy measurements reveal the formation of 2H-phase MoTe2 films. Further, transmission electron microscopy and X-ray photoelectron spectroscopy studies indicate a three-atomic-layer structure and the surface element composition of MoTe2 films. In this study, we mainly focus on the influence of metal contacts attached to the films on their electrical performance. We fabricate 2H-phase-MoTe2-based field-effect transistors (FETs) with various metal contacts such as titanium/gold, nickel and palladium, which present p-type semiconductor properties. We also examine the influence of the work functions of the contact metals on the electrical properties of three-atomic-layer-MoTe2-based FET devices. For a p-type MoTe2 semiconductor, higher work functions of the contact metals afford narrower Schottky barrier heights (SBHs) and eventually highly efficient carrier injection through the contacts.