Abstract: For the analysis of free-edge effect of laminates, the out-plane stresses obtained by displacement solid finite element usually cannot guarantee the requirement of continuity between layers, and the out-plane stress values on the surface are not exactly same with the actual values, so the accuracy of numerical results of displacement finite element method is low. Based on the noncompatible generalized mixed variational principle, noncompatible generalized partial mixed element had been proposed, and had been used for the analysis of the free-edge effect of different ply laminates. By using the characteristics of the noncompatible generalized partial mixed element, which could introduce the boundary conditions of displacement and stress at the same time, solve the displacement and out of plane stress at the same time, the more accurate out-plane stress results at the free-edge are obtained with less computational cost. The numerical example shows that with sparser mesh, the noncompatible generalized partial mixed element predicts the high stress gradient of out-plane stresses near the free-edge accurately. At the same time, the accuracy of singularity is better than the literature results.