This article deals with the solute transport in a single fracture with the combination of the Lattice Boltzmann Method (LBM) and Modified Moment Propagation (MMP) method, and this mixed method is proved to have several advantages over the LBM and Moment Propagation (MP) mixed method which leads to negative concentrations under some conditions in computation. The disadvantage of LBM/MP has been overcome to a certain extent. Also, this work presents an LBM solution of modeling single fractures with uniformly or randomly distributed grains, which can provide a new path of applying the LBM in solute transport simulation in fractures.