A rigorous expression is derived for the shape of a Doppler-broadened absorption cross section. When &Ggr;(E) is assumed to be constant, the expression, which is rigorous for a Maxwellian gas of resonance-absorber atoms, is written as the difference of the two Ψ-functions. The results obtained by the present method are compared with those of the Ψ-function approximation, which is in general use, and the accuracy of the latter approximation is discussed. Comparisons are also made of the low-lying resonances of 235U, 239Pu, 167Er, and 155Gd by numerical computations. For the low-lying resonances, it is shown that the Doppler-broadened absorption cross section is easily computed by the well-known asymptotic expansion of the Ψ-function.