Abstarct: Air which passes from the airway into the lungs is often polluted with a variety of particles, fungi and bacteria that may become deposited in the airways. The airway surface liquid (ASL), is a thin laxyer of fluid covering the luminal surface that plays an important defensive role against foreign particles and chemicals entering the lung. Indeed, the ASL exhibits a two-laxyer structure. The upper laxyer consists of highly viscous and non-Newtonian mucus, which is a nonhomogeneous, viscoelastic fluid containing water, salt and glycosylated mucin proteins and the lower laxyer is a watery lubricating fluid, or ‘periciliary liquid’ (PCL). The cilia, which are hair-like structures, are embedded in PCL with only the tips of the cilia contacting mucus laxyer. In this study, two dimensional numerical model baxsed on hybrid Finite difference-lattice Boltzmann method is used to study the muco-ciliary transport process. Immerse boundary method is used to study the propulsive effect of the cilia and also the effects of mucus–periciliary laxyer interface. The main contribution of this study is on elucidating the role of the viscoelastic behavior of mucus on the muco-ciliary transport and for this purpose an Oldroyd-B model is used as the constitutive equation of mucus for the first time. Numerical simulations have been performed to investigate the effects of mucus viscosity, viscosity ratio, relaxation time, depth of cilia, cilia beat frequency, depth of PCL and mucus and surface tension of the PCL-mucus interface on muco-ciliary transport process. For the standard parameters set, at the specific value of mucus viscosity, mucus viscosity ratio has a great effect on the mean mucus velocity. Enhancing cilia beat frequency is the second parameter that can increase mucus flow. Other parameters do not have a great effect on the mucus flow in this condition. The results also show that at the lower values of viscosity ratio, viscosity of mucus has a great effect on the muco-ciliary transport process and also mucus velocity is affected by mucus relaxation time when its value is less than 0.002 s. Results also indicate that the variation of these properties on the mucus velocity at lower values of viscosity ratio is more significant.