The theory of thermodynamic properties of two-band superconductor with reduced den- sity of charge carriers is developed on the basis of phonon superconducting mechanism with strong electron-phonon interaction. This theory is adapted to describe the behavior of critical temperature TC, energy gaps Δ1, Δ2, and the relative jump of electron specific heat (CS-CN)/CN in the point T = TC along with the variation of charge carrier density in the compound MgB2 when substitutional impurities with different valence are introduced into the system. It is shown, that according to the filling mechanism of energy bands which overlap on the Fermi surface, the quantities TC, Δ1, Δ2 decrease when this compound is doped with electrons and remain constant or weakly change when the system is doped with holes. The theory qualitatively agrees with the experimental data. It is also shown that the consideration of inter- and intraband scattering of electrons on impurity potential improves this agreement.