An InP/InGaAs double heterojunction bipolar transistor (DHBT) with an undoped emitter tunneling barrier and composite collector structure is fabricated and studied. Due to the mass filtering effect for holes, a thin in P tunneling barrier can be used to replace the wide-gap emitter. Experimentally, an appropriate tunneling barrier thickness of 150Å is employed to achieve good IV characteristics, In addition, in GaAsP compositionally step-graded layers are introduced between the p-InGaAs base and n-InP collector. By modulating the bandgap energy of InGaAsP, the large base-collector (B-C) potential spike can be divided into several small spikes with lower barrier height. The 4000Å InP collectors with InP/InGaAsP/InGaAs step-graded junction achieve high breakdown voltages of 14.6V. A small offset voltage of 80mV and a small saturation voltage of 1.8V at the collector current level of 5mA are obtained. Prior to the current gain fall-off caused by the self-heating effect, the step-graded DMBT has the current gain as high as 118 at Ic = 30mA and Vce = 3V.