Abstract: Based on the AF2 scheme and the multiple grid scheme, a fast implicit multigrid approximate factorization scheme (MAF) for solving the three-dimensional conservative full potential equation has been developed and is presented in this paper. The new MAF scheme has been used to solve the three-dimensional transonic flow within DFVLR axial-flow single-stage compressor rotor, and the computed results have been compared with the DFVLR data and the results computed by AF2 scheme.