A gas turbine engine (100) with - a compressor section (105), - a combustor section (106) comprising at least one combustor (107, 110), - a turbine section (112), - at least one gaseous fuel supply conduit (22) with an upstream section (23) and a downstream section (25) the downstream section (25) being connected to the combustor (107, 110) for delivering gaseous fuel and - a fuel booster located in the gaseous fuel supply conduit, the fuel booster (1) having a driving expander (9) with a driving fluid inlet (11) that is in flow connection with a compressed air outlet (116) of the gas turbine engine's compressor, for receiving compressed air and a driving fluid outlet (13) for discharging expanded air and a fuel compressor (17) with a low pressure fuel inlet (19) connected to the upstream section (23) of the gaseous fuel supply conduit (22) and a high pressure fuel outlet (21) connected to the downstream section (25) of the gaseous fuel supply conduit (22), characterised in that a heat exchanger (3) is present which is located such between the unexpanded driving fluid or the expanded driving fluid on the one side and the low pressure gaseous fuel or the high pressure gaseous fuel on the other side that a heat transfer between the air and the gaseous fuel is possible.