Laser peening (LP) induces high-magnitude compressive residual stresses in a small region of a component. The compressive residual stresses cause plastic deformation that is resistant to fatigue fracture. Fatigue cracks are generally nucleated at critical areas, and LP is applied for those regions so as to delay the crack initiation. Many critical regions are located on the edge of the curved portion of structures because of stress concentration effects. Several investigations that are available for straight components may not give meaningful guidelines for peening curved components. Therefore, in this paper, we investigate residual stress behaviors induced by LP along the edge of curved models. Three curved models that have different curvatures are investigated for peening performance. Two types of peening configurations, which are simultaneous corner shot and sequential corner shots, are considered in order to obtain compressive residual stresses along an edge. LP simulations of multiple shots are performed to identify overlapping effects on the edge portion of a curved model. In addition, the uncertainty calculation of residual stress induced by LP considering laser pulse duration is performed.