Inelastic electron tunneling spectroscopy (IETS) is a powerful experimental tool for studying the molecular and metal contact geometries in molecular electronic devices. A first-principles computational method based on the hybrid density functional theory is developed to simulate the IETS of realistic molecular electronic devices. The calculated spectra of a real device with an octanedithiolate embedded between two gold contacts are in excellent agreement with recent experimental results. Strong temperature dependence of the experimental IETS spectra is also reproduced. It is shown that the IETS is extremely sensitive to the intramolecular conformation and the molecule-metal contact geometry changes. With the help of theoretical calculations, it has finally become possible to fully understand and assign the complicated experimental IETS and, more importantly, provide the structural information of the molecular electronic devices.