An investigation into damage onset is presented for unidirectional CFRP laminates which contain fiber discontinuities. Complex carbon fiber composite geometry manufactured using prepregs accompanies fiber discontinuities that result from prepreg cutting. Unidirectional CFRP laminates with 2, 4 and 6-ply discontinuity out of 8 plies are loaded in tension, and show lower fracture stress with more discontinuous plies though fracture strains are almost the same. Non-linear strain behavior just above the discontinuity and discontinuous strain behavior at 20mm away from the discontinuity are found to correspond to onset of crack in resin rich part at discontinuous fiber tip and interlaminar delamination between continuous and discontinuous plies, respectively. Onset stress of these cracks and delamination decreases with the number of discontinuous plies. A shear-lag analysis model that represents the fiber discontinuity in the laminates is proposed, and it is confirmed that obtained stress distribution agrees with that calculated by finite element analysis. Furthermore, it is identified that the onset stress of the two damage modes can be predicted by the shear-lag analysis in which energy release rate is incorporated.