The theoretical method for calculating the dynamic polarizability of monovalent atoms by the variationally stable procedure is given. On this basis, the calculation program is independently developed by us. As an application, the dynamic polarizabilities at different frequencies are calculated with hydrogen atoms as an example, by this program. The calculation results are compared with the Green function data in the literature, with good consistency. The convergence of the variationally stable procedure is analyzed, and the corresponding tune-out wavelength is further determined by using the polarizability calculated in the present work.