Undesirable side effects in patients with a LVAD (Left Ventricular Assist Device) pump fitted include blood damage, thrombosis, blood traumatisation, and End-Organ Disfunctions. These side effects have generally been attributed to the high wall shear stresses and the induced turbulent flow. In this study, we introduce a novel design to address these effects by lowering the rotational speed and providing an optimum flow path design to minimise blood damage. We present an initial scheme for a new Intra-Aortic Shrouded Rotary Axial Pump and develop a sequence of pump geometries, for which the Taguchi Design Optimisation Method has been applied. We apply CFD tools to simulate the pressure rise, pump performance, hydraulic efficiency, wall shear stress, exposure time and mass flow rate. A prototype pump has been tested in a mock cardiovascular circuit using a water-glycerol solution. The optimum design delivered the desired pressure/mass flow rate characteristics at a significantly low rpm (2900 rpm). As a result, the estimated blood damage index is low, matching the design requirements. The theoretical performance was matched by experimental results.