The ESS Radio-Frequency Quadrupole (RFQ) will accelerate and bunch proton beams from 75 keV at the source exit to 3 MeV before the Drift Tube Linac (DTL) entrance. The beam current is 50 mA (75 mA as an upgrade scenario) for 4 % duty cycle. The present document describes the design strategy and the beam dynamics optimization of the pole tip geometry profile. The proposed RFQ is a 4 vane-type structure running at 352.21 MHz of roughly 5 m in length divided in 5 segments of 1 m each. The peak electric fields on the vane surface has been limited to a Kilpatrick value [14] of 1.8. A transmission of more than 99 % is foreseen for the nominal current and high quality beams will be delivered to the subsequent RF structures of the linear accelerator (linac).