The results are presented on the total cross sections, astrophysical S-factor, reaction rate of the deuteron radiative capture on 3He at the temperatures from 0.03 up to 3 T9 calculated in the framework of the potential cluster model with the forbidden states coming from the classification of the orbital states by the Young diagrams. Within the used model and exploited Young diagram classification made it possible to reproduce the general features of the available experimental data on the cross section and reconstructed astrophysical S-factor in the energy range from 200 keV up to 1.4 MeV. The parametrization of the obtained reaction rate has been found and been compared with some other actual reactions with light clusters.