A compound parabolic concentrator (CPC) is a nonimaging concentrator that can concentrate solar radiation coming within its acceptance angle. A low concentration CPC photovoltaic system has the advantages of reduced Photovoltaics (PVs) cell size, increased efficiency and stationary operation. The acceptance angle of a CPC is associated with its geometrical concentration ratio, by which the size of PV cell could be reduced. Truncation is a way to increase the actual acceptance angle of a mirror CPC, but it also reduces the geometrical concentration ratio. On the other hand, a solid dielectric CPC can have a much larger acceptance angle, but it has a larger weight. To overcome these drawbacks, this study presents a novel lens-walled CPC that has a thin lens attached to the inside of a common mirror CPC or has the lens to be mirror coated on its outside surface. The shape of the lens is formed by rotating the parabolic curves of a CPC by a small degree internally around the top end points of the curves. The refraction of the lens allows the lens-walled CPC to concentrate light from wider incidence angle. The commercial optical analysis software PHOTOPIA is used to verify the principle of the presented lens-walled CPC and examine its optical performance against the common CPCs. As an example, the simulation is aimed to evaluate whether a lens-walled CPC with a geometrical concentration ratio of 4 has any advantage over a common CPC with a geometrical concentration ratio of 2.5 in terms of actual acceptance angle, optical efficiency and optical concentration ratio.