The work focuses on the conceptual design and numerical analysis of a four-stage centrifugal pump for the fuel system of a turbofan engine with liquid hydrogen as fuel. Liquid hydrogen is challenging at high pressures due to its special fluid properties. The design condition for the pump is set at take-off, to raise the pressure of liquid hydrogen from 6 bars at the outlet of low-pressure pump to 75 bars, with the rotational speed at 130,000 rpm. While at the cruise condition, the pressure of the fluid is raised from 6 to 19 bars. The pump is designed of centrifugal type with four stages, while all of the stages of the pump are driven by the same shaft. The first stage of the pump is optimized at take-off to avoid cavitation and the remaining three stages have similar design. Numerical analysis of the initial design of the four-stage pump at take-off condition shows that the first stage of the pump performed satisfactorily and raises the pressure of the fluid close to the design value, however stalling is present in the remining three stages which highlight the requirement for further improvements in future investigations.