The dynamics of stochastic Holling-Tanner model with noises were discussed.The noises can be considered as the flood, tsunami, earthquake, drought, large-scale infectious disease, volcanic eruptions and climate warming etc, and they can produce sudden, discrete and large stochastic perturbations.It is shown that the stochastic Holling-Tanner model with noises admits a unique positive global solution starting from the positive initial value.Then, sufficient conditions of the persistence in the meaning of time average and the extinction of the model were obtained by making use of the stochastic comparison theorem and martingale theory etc.The above conclusions show that Levy noises have significant effects on the persistence and extinction of the population, which can even make the long-time dynamic behavior of the population model change fundamentally.Numerical simulations were carried out to illustrate the influence of Levy noises on the population.