This thesis presents the results of a design optimisation of an inducer for a rocket engine turbopump. Its main goal was to optimise a shape of the inducer blades to enlarge an operating range of the entire pump that is limited by cavitation. The blade was parameterised with four parameters: sweep angle, sweep radius, incidence angle and blade solidity at the tip. The performance of the given pump design is evaluated with a two-phase CFD simulation. The optimisation process is based on a surrogate model that interpolates the simulation results in the entire design space from a fixed number of samples. The results show 17% improvement of the suction performance, which is caused by reduced vapour volume in the flow channel and higher inducer head. Sweep radius proved to be the most important parameter as it increases the minimal pressure at the leading edge.