We propose a microscopic model in order to investigate the multiferroic properties of CuBr2 in dependence on temperature, size, magnetic field and ion doping. Using a Green’s function technique we have calculated the magnetization, the heat capacity, the polarization and the dielectric constant. The specific heat has at the magnetic transition temperature TN a clear peak which disappears by applying an external magnetic field h. The polarization increases whereas the dielectric constant decreases with increasing h due to strong magnetoelectric coupling. In a CuBr2 nanoparticle appears a weak ferromagnetism due to the uncompensated spins on the surface. The magnetization increases with decreasing nanoparticle size. The Neel temperature rises strongly applying by ion doping a compressive strain and decreases by a tensile strain.