An efficient particle dispersion model (SPEED) was described for predicting dilute turbulent two-phase flows in non-orthogonal grids. The continuous-phase flow field was modeled using the Reynolds-stress transport model whereas the particular flow field was modeled using the Lagrangian trajectory model. The two phases are linked with each other via two-way coupling sources. A robust numerical algorithm was developed to determine the spatial distribution of physical particles in irregular Eulerian control volumes. The SPEED model requires tracking a small number of particle trajectories to achieve a stochastically significant solution. The present paper has focussed on how to implement the SPEED model in body-fitted coordinates. To validate the model, some demonstrative results are presented and compared with the experimental measurements for a particle-laden turbulent gas flow.