In this paper, Analysis of the stability and solitary waves for a car-following model on two lanes is carried out. The stability condition of the model is obtained by using the linear stability theory. We study the nonlinear characteristics of the model and obtain the solutions of Burgers equation, KDV equation, and MKDV equation, which can be used to describe density waves in three regions (i.e., stable, metastable and unstable), respectively. The analytical results show that traffic flow can be stabilized further by incorporating the effects come from the leading car of the nearest car on neighbor lane into car-following model.