In the study of convective diffusion of aerosol in a horizontal rectangular channel under laminar flow, the effect of axial Brownian diffusion on aerosol transport and deposition is considered and analyzed theoretically. The general explicit solutions for particle concentration and penetration are obtained by theoretical derivation, and the correctness of the result is verified by comparing with the previous studies. With considering the axial diffusion, the influence of the Peclet number on the concentration distribution and penetration of aerosol particles has been investigated.The results show that the axial Brownian diffusion is negligible when the Peclet number is greater than 700 for considering the distribution of aerosol concentration, while it is 500 for considering the penetration rate. The conditions for determining whether axial diffusion can be ignored are based on the ratio of channel length to half-height, deposition parameters and Peclet number. This provides an important theoretical basis for understanding the aerosol transport mechanisms in the pipeline.