Abstract Electron acceleration by a localized r.f. field is considered as a mechanism to fill the spectrum gap in lower hybrid current drive (LHCD). A simple one-dimensional model along the magnetic lines of force has been employed. The electron dynamics have been studied by numerically solving the equation of motion in a model localized r.f. field for a given initial distribution of test electrons. Special attention is focused on analyses for the interaction between the r.f. field and the electrons, whose initial velocity is well below the phase velocity of the wave to understand the acceleration mechanism. Moreover, model calculations have been performed using realistic wave parameters (localized width, wave number etc.) for typical LHCD experimental conditions in both medium and large tokamaks to examine whether or not the mechanism considered here is a possible solution to fill the spectrum gap.