Numerical simulations based on a novel band-to-band tunnelling model and DC quasi-stationary method have been performed for a field-induced inter-band tunnelling effect transistor with a degenerately doped floating body and source/drain tunnel junction. Carrier injection through the tunnel junctions into a floating body is responsible for negative-differential conductance as well as negative-differential trans-conductance. Simulation results for various device structures show that a gate field-effect on the tunnel junctions is a key design factor to improve device characteristics.