A curved secondary battery may include a can having an opening, an electrode assembly accommodated in the can, and a cap plate coupled to the can. The cap plate may include a concave first side surface and a parallel convex second side surface, and a first surface and a second surface that connect the first and second side surfaces. The first surface may include a first groove extending along a lengthwise direction of the cap plate and positioned closer to the first side surface than to the second side surface.