A hybrid frame sleeve case for a portable electronic device is disclosed herein. The portable electronic device may be a laptop computer, a tablet, or another portable electronic device. The case may include flexible panels, such as neoprene or fabric panels, attached to an elastic polymer frame, such as ethylene vinyl acetate (EVA). The elastic polymer frame extends around a perimeter of the sleeve to provide cushioning or padding for the side edges of the sleeve. A magnetic latch or other latch may be used to secure an opening on one side of the sleeve. The case may optionally include a charging system that allows the portable electronic device to be charged while housed in the case or otherwise positioned to allow charging by the charging system.