In this paper, we present a Terahertz (THz) Travelling-Wave-Amplifier (TWA) design using a Ballistic Deflection Transistor (BDT). The BDT is an emerging functional device based on InGaAs/InAlAs/InP, which can operate at THz frequencies. A transistor model is proposed, based on data provided by Monte Carlo simulation. We have developed a new nearly lossless THz transmission line (0.46dB/mm over 0.8-1.5THz simulated in ANSYS HFSS), called Parallel Plate Dielectric Waveguide with Signal line (PPDWS), and we are able to design a 24-stage BDT TWA with an ADS simulated gain over 10dB at 1-1.5THz. This THz BDT amplifier design opens up new possibilities by increasing the speed by 100 times compared to existing technologies.