In this paper, an improved numerical scheme based on the lattice BGK method (LBM) is proposed for solving the advective transport equation coupled with an incompressible flow. We utilize the LBM to solve the equations of flow field and build a second order discrete scheme for the advective transport equations using the probability density function of LBM. Meanwhile, the validity of the method is verified by an advective transport in a planar channel flow. Numerical results show that the method reduces the numerical dissipation efficiently and it involves consistently smaller memory requirements compared with previous studies.