DEMO (DEMOnstration Fusion Power Plant) is a proposed nuclear fusion power plant that is intended to follow the ITER experimental reactor. The main goal of DEMO will be to demonstrate the possibility to produce electric energy from the fusion reaction. The injection of high energy neutral beams is one of the main tools to heat the plasma up to fusion conditions. A conceptual design of the Neutral Beam Injector (NBI) for the DEMO fusion reactor, is currently being developed by Consorzio RFX in collaboration with other European research institutes. High efficiency and low recirculating power, which are fundamental requirements for the success of DEMO, have been taken into special consideration for the DEMO NBI. Moreover, particular attention has been paid to the issues related to reliability, availability, maintainability and inspectability. A conceptual design of the beam source for the DEMO NBI is here presented featuring 20 sub-sources (two adjacent columns of 10 sub-sources each), following a modular design concept, with each sub-source featuring its radio frequency driver, capable of increasing the reliability and availability of the DEMO NBI. Copper grids with increasing size of the apertures have been adopted in the accelerator, with three main layouts of the apertures (circular apertures, slotted apertures and frame-like apertures for each sub-source). This design, permitting to significantly decrease the stripping losses in the accelerator without spoiling the beam optics, has been investigated with a self-consistent model able to study at the same time the magnetic field, the electrostatic field and the trajectory of the negative ions. Moreover, the status on the R&D carried out in Europe on the ion sources is presented.