Abstract: The transfer of ¹⁴⁰Ba from nucler explosion in the atmosphere is analyzed theoretically in the paper. Fokker-Planck equation of Markov processes is resulted in, which is from Ito stochastic differential equation. Eulerian advection-diffusion equation and Lagrangian stochastic equation are proved to be equal. The latter is the basic of stochastic Monte-Carlo method. Turbulence parameterizations of radionuclides transferring in the atmosphere are researched. Horizontal and vertical turbulence parameterizations of eddy diffusivities, friction velocity and length of Monin-Obukhof are involved. The fission yield of ¹⁴⁰Ba from ²³⁹Pu is also studied. The decay chain equation is solved. An activity distribution varying with time of ¹⁴⁰Ba source from explosion of 1 kt TNT yield plutonium bomb is got. After numerical results are simulated, some equivalent value figures about the activity of ¹⁴⁰Ba per unit volume dependent upon space and time are given. Meanwhile, terrain data and meteorological data are taken into consideration.