The multiscale finite volume (MSFV) method is extended to account for non-matching coarse grids arising from faulted porous media. To obtain accurate quantities at the coarse scale, basis and correction functions are computed in extended local domains near the fault regions. With the new framework it is shown that the MSFV results are very close to the fine-scale reference solutions. Finally, to improve the quality and to extend the applicability of the framework, an iterative MSFV method for faulted reservoirs is devised; similar to the recently proposed i-MSFV method for conforming coarse grids by Hajibeygi et al. (2008). Convergence histories of the new i-MSFV method are shown for different homogeneous and heterogeneous test cases. It is concluded that this extension of the MSFV method is very flexible and allows to deal with complex geometries such as faulted reservoirs.@en