Diverse phenomena in physical, chemical, and biological systems exhibit significant stochasticity and therefore require appropriate simulations that incorporate noise explicitly into the dynamics. We present a lattice kinetic Monte Carlo approach to simulate the trajectories of tracer particles within a system in which both diffusive and convective transports are operational. While diffusive transport is readily accounted for in a kinetic Monte Carlo simulation, we demonstrate that the inclusion of bulk convection by simply biasing the rate of diffusion with the rate of convection creates unphysical, shocklike behavior in concentrated systems due to particle pile up. We report that elimination of shocklike behavior requires the proper passing of blocked convective rates along nearest-neighbor chains to the first available particle in the direction of flow. The resulting algorithm was validated for the Taylor–Aris dispersion in parallel plate flow and multidimensional flows. This is the first generally applicable lattice kinetic Monte Carlo simulation for convection-diffusion and will allow simulations of field-driven phenomena in which drift is present in addition to diffusion.