We present quantum mechanical self-consistent calculations on the transfer characteristics of a new resonant tunneling transistor. The model structure consists of a source, a tunneling barrier, a quantum-well drain, a thick insulator, and a backgate. The tunneling barrier consists of a double-barrier structure. We demonstrate that based on energy and momentum conservations, the transistors display oscillatory negative transconductance, as the gate can control the resonant tunneling probability between source and drain. With the inclusion of a realistic energy relaxation time of approximately 0.1 ps, the double-barrier resonant tunneling transistor shows an enhancement of the tunneling current density and the negative transconductance feature is only slightly changed. We also find that the quantum-well drain is not able to completely screen the electric field imposed by the backgate bias as a result of limited density of states of two-dimensional systems.