A three-dimensional particle method for the diffusion of matter in a round jet is proposed. The flow field is calculated with a vortex method, whereas the concentration field is simulated through a method analogous to the vortex method. The particle method is based on the Lagrangian approach; thus no computational grids are needed. It is applied to simulate the diffusion of matter in a compound round jet. The large-scale eddies, appearing just downstream of the disappearing point of the potential core, cause the diffusion of matter in the radial direction. In the subsequent developed region of the velocity field, the diffusion proceeds to the smaller vortical structure. The mean concentration and the concentration fluctuation intensity are in the self-preservation state at x/D greater than or equal to 8 and x/D greater than or equal to 13, respectively. These numerical results are favorably compared with experimental ones, indicating that the present particle method is usefully employed to simulate the diffusion of matter in a round jet. (C) 2004 Elsevier Ltd. All rights reserved.