A lattice Boltzmann flux solver (LBFS) is presented for simulation of fluid flows. Like the conventional computational fluid dynamics (CFD) solvers, the new solver also applies the finite volume method to discretize the governing differential equations, but the numerical flux at the cell interface is not evaluated by the smooth function approximation or Riemann solvers. Instead, it is evaluated from local solution of lattice Boltzmann equation (LBE) at cell interface. Two versions of LBFS are presented in this paper. One is to locally apply one dimensional compressible lattice Boltzmann (LB) model along the normal direction to the cell interface for simulation of compressible inviscid flows with shock waves. The other is to locally apply multi dimensional LB model at cell interface for simulation of incompressible viscous and inviscid flows. The present solver removes the drawbacks of conventional lattice Boltzmann method (LBM) such as limitation to uniform mesh, tie-up of mesh spacing and time interval, limitation to viscous flows. Numerical examples show that the present solver can be well applied to simulate fluid flows with non-uniform mesh and curved boundary.