The structural characteristics of multilayered interior permanent magnets, magnetic bridges, and flux barriers contribute to a remarkable saturation effect in permanent magnet assisted synchronous reluctance motors (PMaSynRMs), whereas the analytical calculation of the magnetic field and electromagnetic performance for PMaSynRMs considering the saturation effect remains to be a knotty problem. This article proposes a nonlinear analytical model (AM) to predict the magnetic field and electromagnetic performance of a PMaSynRM under the saturation effect. First, the studied PMaSynRM is reshaped to an equivalent concentric annular structure. Second, the technique of harmonic modeling is employed to obtain the analytical solution for the Maxwell field governing equations in each solution region. Finally, considering features of the complex motor structure, an adaptive convergence rate iterative algorithm is improved for the calculation of the saturation effect. To verify the feasibility and the accuracy of the proposed method, the analytical predictions of the magnetic flux density and the electromagnetic performance have been compared with finite element method analysis results. Meanwhile, the reasonable selection of the harmonic truncation order number has been discussed. The proposed nonlinear AM can consider the magnetic saturation and cross-saturation effect accurately, which is suitable for performance predictions and parametric studies of PMaSynRMs.