In this paper, we present a new and highly efficient solar concentrating mirror. It is composed of partial high-order cylinder inner wall which is determined by two sets of specific coefficients a2, a4, a6, a8, a10, a12, a14, a16 and C. According to the higher-order cylindrical equation and the optical law of reflection, the relationship between the direction vectors of sunbeams reflected from the cylindrical inner wall and the coefficients of a higher order polynomial equation, a2,a4, a6, a8, a10, a12, a14, a16 and C is derived. By optimizing these coefficients, all sunbeams incident on the inner wall of higher-order cylinder can be reflected and focused into a very thin line segment parallel to the cylindrical busbar, which means line focus. Two sets of particular coefficients associated with the high- order cylindrical surface are obtained by using particle swarm optimization algorithm. The focusing effect of the solar concentrating mirror, defined by the particular set of coefficients, is demonstrated by using computer simulations. The concentrator mirror has a light compression ratio of about 148 : 1 and its linear spot can be used as a strong light source or a high temperature heat source. The higher-order cylindrical mirror can be made of metal or glass in three steps: cutting, grinding, and polishing, and may also be formed by a higher order cylindrical framework and an aluminized polyester film laid on the framework.