In this study, damage behavior of curved carbon fiber reinforced polymer (CFRP) composite laminates that are important sub-structures (ribs, shear webs and spar flanges etc.) for wind turbine blades are investigated under static and fatigue loading conditions. Cross-ply curved specimen consisting of groups of three 0 degrees and 90 degrees layers is used for clear observation of the matrix cracking in thicker plies. Damage mechanisms and locations under static and fatigue loadings are examined. In the experiments, failure is found to initiate in the first group of 90 degrees layers under static loading while it is found to occur in the second group of 90 degrees layers under fatigue loading. The overall goal of the project is to contribute to development of design techniques or local reinforcement methods to increase fatigue life and durability of these curved sub-structures used in wind turbine blades.