Inelastic tunneling spectroscopy (IETS) in combination with scanning tunneling microscopy (STM) is a powerful method to investigate electronic spectrum and transport properties of large molecules. We consider theoretically nonequilibrium electronic transport through a single molecule placed between a conducting substrate and an STM tip at finite voltages. A semi-empirical tight-binding model is used to describe linear molecules (as DNA). The STM based molecular junction is considered as a strongly asymmetric double tunnel junction. The molecule is weakly coupled to the substrate and to the STM tip. The coupling of the different parts of the molecule to the STM tip is a function of the distance, which results in a tunneling current dependence on the position of the STM tip (STM image of the molecule). In the limit of small voltages the conductance of nonmetallic molecules is very small and determined by environ-mentally induced states. At finite voltages resonant transport through molecular orbitals gives peaks in the differential conductance as a function of the voltage. The nonequilibrium Green function method is applied to calculate the contribution of different molecular orbitals at finite voltages. It is shown that molecular spectra are modified by charging and vibrational effects.