A method of evaluating the density of states N(E) of a lattice containing impurity atoms is presented. A generalized Green's function is introduced in order to take into account the interaction among energy bands explicitly. Particular attention is paid to the transition region of energy where two energy bands are separated by a gap. In the case of a fixed spatial configuration of impurities, a correction term to N(E) due to impurities as well as the energy of impurity levels are obtained, and the results are applied to one- and two-impurity problems. In the case of a random distribution of impurities, perturbation calculations are employed by the use of a graphical method. N(E) is shown to be expressed by an integral representation of N0(E), where N0(E) is the density of states of the regular lattice. It is shown that (1) when the strength of the impurity potential is weak, the curve of N(E) is tailed off into the forbidden region, (2) when it is so strong that it causes impurity levels, an impurity band takes place. A criterion for the appearance of the impurity band and for the band gap is obtained. Approximate forms of the curve of N(E) near the bottom or the top of the impurity band as well as of the main continuum are studied.