In this talk, we present the recently developed cell-average based neural network (CANN) method. The method is motivated by finite volume scheme and is based on the integral or weak formulation of the PDEs. A simple feed forward network is forced to learn the solution average difference between two neighboring time steps. Well trained network parameter set is identified as the scheme coefficients of an explicit one-step finite volume type method. The CANN method is implemented as a regular finite volume scheme, thus is mesh dependent. Different to conventional numerical methods, CANN method can be relieved from the explicit scheme CFL restriction thus can adapt large time step size for solution evolution forward in time. CANN method can sharply evolve contact discontinuity with almost zero numerical diffusion. Shock and rarefaction waves are well captured for nonlinear hyperbolic conservation laws.