Resonant tunneling in step-barrier structures is investigated by using the transfer-matrix technique. The formulas for the transmission coefficient and the current density are derived when taking into account the coupling between components of the motion of an electron in directions parallel and perpendicular to the interfaces. By making a detailed comparison of resonant tunneling among single square-barrier structures, asymmetric double-barrier structures, and step-barrier structures, the tunneling properties in step-barrier structures are revealed. It is shown that the global behavior of step-barrier structures obtained resembles that of asymmetric double-barrier structures, and step-barrier structures are superior to both single- and double-barrier structures in many aspects. In comparison to asymmetric double-barrier structures, step-barrier structures have several features, such as a wider negative-differential resistance region, easier fabrication, high-speed response, and a relatively lower transmission coefficient and current peak-to-valley ratios. Moreover, higher resonant bias is required in order to obtain optimal transmission resonances in the step-barrier structure. The results shown in this work not only shed new light on the physics of resonant tunneling in electric-barrier structures but are also helpful in designing quantum devices based on step-barrier tunneling structures.