Abstract: To address the overly conservative predictions of traditional first-ply failure (FPF) methods and the low computational efficiency and poor convergence of progressive damage methods (PDMs) in the strength prediction of composite laminates containing geometric features such as open holes and bends, a three-dimensional (3D) progressive damage analysis method based on first-ply fiber failure is proposed. The method adopts a decoupling strategy between fiber failure determination and non-fiber damage evolution: matrix damage, interlaminar damage, and other non-fiber damage modes cause only local stiffness degradation and stress redistribution, whereas the overall failure determination of the laminate is governed primarily by fiber failure. Within a 3D stress framework, the safety margin is introduced as the failure assessment index. Based on the Yamada-Sun criterion, a fiber failure criterion accounting for the contribution of longitudinal shear stresses is established, while non-fiber damage criteria are constructed with reference to the simplified Puck criterion. T800 carbon fiber/PN resin composite laminates are investigated, and static tests together with finite element analyses are conducted for open-hole and L-shaped laminates under tensile, compressive, and four-point bending conditions. The results show that, in terms of strength prediction, when the contribution of longitudinal shear stress is neglected, the relative errors of the predicted failure loads range from −33.3% to −4.8% for the tensile and compressive cases. When the contribution of longitudinal shear stress is fully considered, the absolute relative errors of the predicted failure loads for all four loading cases are reduced by 7.4–39.5 percentage points compared with those obtained using the traditional FPF method. In terms of computational efficiency, the computational times for the L-shaped laminate under compression and four-point bending are only 8.6% and 35.4% of those required by the 3D Hashin PDM, respectively. The proposed method retains a conservative prediction tendency while achieving lower computational cost and better solution stability, thereby providing an efficient approach for the strength assessment of composite structures.