In this paper, a two-layer model with dispersive and dissipative effects but without Coriolis effect is investigated. It is proved that in the model, under certain parameter conditions, there exists monotone travelling wave as well as oscillation travelling wave in addition to the nonlinear periodic solution ad solitary wave. The conditions for their existence are provided. It is particularly pointed out that the pattern of the oscillation travelling wave is similar to that of the pressure upwelling wave of a squall line which passes certain region.