It is known that theory of MOND (Modification of Newtonian Dynamics) with spherical symmetry cannot account for the convergence kappa-map of Bullet Cluster 1E 0657-558. In this paper, we try to set up a Finslerian MOND, a generalization of MOND in Finsler space-time. We use Ric = 0 to obtain the gravitational vacuum field equation in a 4D Finsler space-time. To leading order in the post-Newtonian approximation, we obtain the explicit form of the Finslerian line element. It is simply the Schwarzschild's metric except for the Finslerian rescaling coefficient f(v) of the radial coordinate r, i.e. R = f(v) r. By setting f (v) = root 1 - (GMa(0)/v(4)), we obtain the famous MOND in a Finslerian framework. Taking a dipole and a quadrupole term into consideration, we give the convergence kappa in gravitational lensing astrophysics in our model. Numerical analysis shows that our prediction is to a certain extent in agreement with the observations of Bullet Cluster 1E 0657-558. With the theoretical temperature T taking the observed value 14.8 keV, the mass density profile of the main cluster obtained in our model is of the same order as that given by the best-fitting King beta-model.