An interesting InP/InGaAs double heterojunction bipolar transistor (DHBT) with a step-graded InAlGaAs/InP collector structure are demonstrated and studied. By use of the step-graded InAlGaAs/InP collector structure at the base-collector heterojunction, the current blocking effect is effectively eliminated. Experimentally, the studied device shows a relatively better common-emitter breakdown voltage and low output conductance though at high temperature. Also, the studied device shows a wider collector current density operation region which over 11 decades in magnitude of collector current density (10-6 to 105 A/cm2). Moreover, the studied device also shows the relatively weaker temperature dependence on the electron impact ionization α. Consequently, the studied DHBT device provides the promise for low-voltage and low-power circuit applications.