L-shaped stiffened composite panels provide an efficient structure for engineering applications. However, they often produce delamination in the preparation and service process due to a series of factors. To study the effect of different types of delamination on the compressive strength of stiffened composite panels, ABAQUS finite element software was used in combine with the progressive damage subroutine user-defined field variable (USDFLD), and the finite element model was established based on cohesive theory to realize the prediction of the progressive failure process and strength of the stiffened composite panels. The results showed that the delamination of a stringer had a greater impact on the strength of the stiffened composite panels than did the debonding between the skin panel and a stringer and the delamination of the skin panel. The debonding delamination and delamination of a stringer exhibited delamination growth near the damage position during static compression, but delamination of the skin panel exhibited no delamination growth. The experimental results were in good agreement with the finite element simulation results, which verified the validity of the finite element model.