Cylindrical vector beams with radial or azimuthal polarization have created great interest due to their unique focusing characteristics and focal components. In this Letter, we investigate second-harmonic general (SHG) of single CdSe nanowires (NWs) excited by tightly focused cylindrical vector beams of 150 fs pulses at 800 nm. With the specific polarizations in the focal region, we demonstrate a three-dimensional interaction between the focal electric field components and the NWs. The excitation anisotropy of the SHG can directly be derived from the imaging patterns with the cylindrical vector beams. The highest SHG excitation efficiency is observed when the polarization is parallel to the long axis of the NW, which is confirmed by the conventional linear polarization approach. Our work with cylindrical vector beams provides a new approach to study the nonlinear phenomenon of single semiconductor NWs in three dimensions and it could be applied to many other nanoscale systems.