The Global Lagrangian Atmospheric Dispersion Model (GLADIM) is described. GLADIM is based on the global trajectory model, which had been developed earlier and uses fields of weather parameters from different atmospheric reanalysis centers for calculations of trajectories of air mass that include trace gases. GLADIM includes the parameterization of turbulent diffusion and allows the forward calculation of concentrations of atmospheric tracers at nodes of a global regular grid when a source is specified. Thus, GLADIM can be used for the forward simulation of pollutant propagation (volcanic ash, radionuclides, and so on). Working in the reverse direction, GLADIM allows the detection of remote sources that mainly contribute to the tracer concentration at an observation point. This property of Lagrangian models is widely used for data analysis and the reverse modeling of emission sources of a pollutant specified. In this work we describe the model and some results of its validation through a comparison with results of a similar model and observation data.