Abstract: Grid fin, also known as lattice control, is a kind of unconventional aerodynamic lifting and control surfaces that consists of an outer frame supporting an inner grid of intersecting planar surfaces with small chord. In this paper an efficient meshing strategy is developed to generate high quality point-to-point multi-block structured grid for such a complex geometry. The N-S equations are solved numerically using the finite volume method on the herein generated multiblock structured grid, adopting multigrid method to accelerate the convergence. With these strategies the flow around a gridfinned missile is simulated at subsonic, transonic and supersonic states, with free stream Mach number ranging from 0.5 to 3. The simulation results show excellent agreement with the experiment data for the aerodynamic forces and moments. Detailed flow field is also obtained that exhibits the complex flow properties inside the grid frame. The results provide an effective means for accurate simulation of grid fin missiles flow fields.