The binding energies of excitons bound to neutral donors in two-dimensional (2D) semiconductors within the spherical-effective-mass approximation, wchich are nondegenerate energy bands, have been calculated by a variational method for a relevant range of the effective electron-to-hole mass ratioσ. The ratio of the binding energy of a 2D exciton bound to a neutral donor to that of a 2D neutral donor is found to be from 0.58 to 0.10. In the limit of vanishing σ and large σ, the results agree fairly well with previous experimental results. The results of this approach are compared with those of earlier theories.