The ITER Neutral Beam Test Facility (PRIMA) is presently under construction at Consorzio RFX (Padova, Italy). PRIMA includes two experimental devices: an ITER-size ion source with low voltage extraction, called SPIDER, and the full prototype of the whole ITER Heating Neutral Beams (HNBs), called MITICA.The purpose of MITICA is to demonstrate that all operational parameters of the ITER HNB accelerator can be experimentally achieved, thus establishing a large step forward in the performances of neutral beam injectors in comparison with the present experimental devices.The design of the MITICA extractor and accelerator grids, here described in detail, was developed using an integrated approach, taking into consideration at the same time all the relevant physics and engineering aspects. Particular care was taken also to support and validate the design on the basis of the expertise and experimental data made available by the collaborating neutral beam laboratories of CEA, IPP, CCFE, NIFS and JAEA. Considering the operational requirements and the other physics constraints of the ITER HNBs, the whole design has been thoroughly optimized and improved. Furthermore, specific innovative concepts have been introduced.