In this study, using a self-consistent model and considering the random phase approximation, we have calculated the screening function of semiconducting zinc oxide (ZnO) and indium arsenide (InAS) nanowires coated by dielectric environment. We show that when these nanowires are coated by high dielectric media (larger than nanowire dielectric) the dielectric function of free charge is reduced inside the nanostructure. However, in a low dielectric media (lower than semiconductor dielectric) the dielectric function is increased. Moreover, the behavior of dielectric function versus the variation of radius, carrier density of nanowire and dielectric media is investigated in liquid helium temperature and in the temperature range of 4-300 K.