The NeoVAD is a proposed paediatric axial-flow Left Ventricular Assist Device (LVAD), small enough to be implanted in infants. The design of the impeller and diffuser blades is important for hydrodynamic performance and haemocompatibility of the pump. This study aimed to optimise the blades for pump efficiency using Computational Fluid Dynamics (CFD), machine learning and global optimisation. Meshing of each design typically included 6 million hexahedral elements and a Shear Stress Transport turbulence model was used to close the Reynolds Averaged Navier–Stokes equations. CFD models of 32 base geometries, operating at 8 flow rates between 0.5 and 4 L/min, were created to match experimental studies. These were validated by comparison of the pressure-flow and efficiency-flow curves with those experimentally measured for all base prototype pumps. A surrogate model was required to allow the optimisation routine to conduct an efficient search; a multi-linear regression, Gaussian Process Regression and a Bayesian Regularised Artificial Neural Network predicted the optimisation objective at design points not explicitly simulated. A Genetic Algorithm was used to search for an optimal design. The optimised design offered a 5.51% increase in efficiency at design point (a 20.9% performance increase) as compared to the best performing pump from the 32 base designs. An optimisation method for the blade design of LVADs has been shown to work for a single objective function and future work will consider multi-objective optimisation.