Use of solar concentration can reduce the size and increase the efficiency of a solar photovoltaic or heating system. A compound parabolic concentrator (CPC) is a non-imaging concentrator that concentrates light coming within its acceptance angle, so it is capable to concentrate both direct and diffuse solar radiation. An east-west orientated CPC with a half acceptance angle of 25° may concentrate most of the annual direct solar radiation when it is tilted at an angle same as the local latitude. The corresponding geometrical concentration ratio is about 2.37, by which the PV size could be reduced. If the CPC geometrical concentration ratio is expected to be 4, the half acceptance angle will be 14.5°. The tilt angle of the CPC will need be adjusted four times to receive most of the annual direct solar radiation. Obviously, this will cause inconvenience in practice. This study presents a novel lens-walled CPC. The thin lens attached to the wall of a CPC may turn the light at a larger incidence angle into a direction within the acceptance angle of the original CPC. The preliminary study has indicated that the actual half acceptance angle of a lens-walled CPC with a geometrical concentration ratio of 4 could be increased from 14.5° to larger than 25°. The optical concentration ratio of the 3D lens-walled CPC may be about 11 at the incidence angle of 5° and about 6 at the incidence angle of 25°.