  A "natural" model for the QCD invariant (running) coupling, free of the IR
singularity, is proposed. It is based upon the hypothesis of finite gluon mass
$ m_{gl}$ existence and, technically, uses an accurate treating of threshold
behavior of Feynman diagram contribution. The model correlates with the
unitarity condition.
  Quantitative estimate, performed in the one-loop approximation yields a
reasonable lower bound for this mass $m_{gl} > 150$ MeV and a smooth IR
freezing at the level $\alpha_s(Q^2)\lesssim 1$.
