A three-dimensional cone-shaped concentrator was designed and analyzed through an approach of coordinate transformation theory. The device can provide varying performances for concentrating along the symmetric axis. The physical picture regarding concentrating ability of this structure was revealed and quantitative analyses were performed for the purpose of investigating the dependence of the concentrating properties on the structural parameters. Moreover, reduced material parameters were theoretically derived and the corresponding mismatched impedance at boundaries was analyzed. Finite element method-based numerical simulations results of the device were further presented to verify our theoretical design. (C) 2008 Optical Society of America.