A new nonlinear dispersion relation is given in this paper,which can overcome the limitation of the intermediate minimum value in the dispersion relation proposed by Kirby and alrymple(1986),and which has a better approximation to Hedges' empirical relation than the modified relations by edges(1987),Kirby and Dalrymple(1987) for shallow water.The new dispersion relation is simple in form, thus it can be used easily in practice.Meanwhile, a general explicit approximation to the new dispersion relation and other nonlinear dispersion relationa is given.By use of the explicit approximation to the new dispersion relation along with the mild slope equation taking into ccount weakly nonlinear effect, a mathematical model is obtained, and it is applied to laboratory ata.The results show that the model developed with the new dispersion relation predicts wave ransformation over complicated topography quite well.