We have studied the quantum transport of electrons in a three-step single-barrier A1GaAs heterostructure under electric field. Using the quantum transmitting boundary method and Tsu-Esaki approach, we have calculated the transmission coefficient and current-voltage characteristic. The difference of the effective mass among the three barriers is taken into account. Effects of the barrier width on transmission coefficient and peak-to-valley current ratios are examined. The largest peak-to-valley current ratio is obtained when the ratio of widths of the left, middle, and right barrier is fixed at 4:2:1. The calculated results may be helpful for designing devices based on three-step barrier heterostructures.