An efficient self-consistent approach combining the nonequilibrium Green's function formalismwith density functional theory is developed to calculate electron transport properties of moleculardevices with quasi-one-dimensional (1D) electrodes. Two problems associated with the lowdimensionality of the 1D electrodes, i.e., the nonequilibrium state and the uncertain boundaryconditions for the electrostatic potential, are circumvented by introducing the reflectionlessboundary conditions at the electrode-contact interfaces and the zero electric field boundaryconditions at the electrode-molecule interfaces. Three prototypical systems, respectively, an idealballistic conductor, a high resistance tunnel junction, and a molecular device, are investigated toillustrate the accuracy and efficiency of our approach.