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The field reconstruction method (FRM) is a recent technique for modeling electrical machines. This method offers the same accuracy as the finite element analysis at a lower computational cost by using a few prestored results, which are known as the basis functions. This paper describes an enhanced three-dimensional (3-D) FRM for modeling an axial flux permanent magnet machine. This machine has a special structure, which warrants the use of 3-D modeling for completely describing its behavior. The proposed method can be an efficient solution for the 3-D modeling of electrical machinery, especially from the viewpoint of time-varying and iterative optimization problems. Experimental and simulation results are provided to validate the proposed method's precision.