L-shaped composite laminates are one of the geometrically complex parts of aircraft. Hence, it is essential to conduct a delamination behavior investigation of L-shaped composite laminates when subjected to impact and cyclic loads, particularly on the sharply curved geometry. In this study, three different loading conditions are implemented sequentially including impact, static, and cyclic by means of the Finite Element Method. The low velocity impact of 1.75 m/s is applied to obtain the delamination distribution by using an explicit simulation scheme. The delamination distribution due to impact is then utilized as the initial condition for static and cyclic loading conditions. By using an implicit simulation scheme, four different configurations are performed by combining positions and directions of the displacement to examine the maximum load bearing capacity of the laminates. Moreover, cyclic loading condition is performed to investigate the fatigue life of the L-shaped laminates. It has to be noted that for cyclic loading, a user material (UMAT) is implemented into the FEM package ABAQUS to include a fatigue constitutive model for cohesive elements. The finite element analyses are carried out using a simplified cyclic loading (SCL) procedure, in which the maximum displacement is kept constant. The results showed that multilayered delamination is initiated due to the low velocity impact. The maximum load bearing capacity, the acceleration of the delamination propagation, and the mode-mixity are mainly influenced by the delamination distributions as well as the displacement configurations.