Carbon diffusion in metals has received a lot of attention and has been the subject of intensive theoretical investigations in recent years. The purpose of this work is development a simple statistical model of the carbon atoms diffusion in the crystal lattice of metals and its application for calculating the diffusion coefficients of carbon atoms in iron and steel. The relationship between the diffusion flux of atoms and the gradient of their chemical potential, as required by non-equilibrium thermodynamics, is obtained from the basic principles of statistical thermodynamics. For a real solid solution of impurity atoms in a metal, an expression is found for the diffusion coefficient, the value of which depends on physical constants, the atomic weight of the solute, the square of the temperature and activity i-element in solid solution. The calculations have a good agreement with the known experimental data on the diffusion of carbon atoms in iron and steels and is higher than in classical atomic diffusion models. The activation energy of carbon diffusion in γ- phase of various steels has values close to 120 kJ. Proposed formula well describes the deviation of the carbon diffusion coefficient from the Arrhenius law at medium and high temperature.