The nonlinear Kelvin travelling-wave solution with orographic slope is shown in this paper.Suppose that the orographic slope is invariable along the mountain range orientation but is variable across it,then analytic solution of the model is obtained,which is favourable for further understanding coastally mountain-trapped wave.Here the solution is compared with typical solution,where lateral boundary is perpendicular and bottom boundary is horizontal surface.It is found that wave speed and perturbation amplitude of the former is smaller than the latter;it is also analogous in some ways to the case of real coastally mountain-trapped wave in Wuyi Mountain of southeast China.