We report the near-field nanofocusing through two types of plasmonic nanostructures consisting of annular grooves and annular slit, respectively. The radius of one half of each circle is designed to be bigger than the other half by half wavelength of the surface plasmon polaritons. By illuminating the structures with linearly polarized light, one single tight focal spot was detected by the scanning near-field optical microscope. Compared with the method of using radially polarized light, this method does not need to keep the center of the illuminating light right on the center of the structure, hence is much easier to use. Furthermore, theoretical simulations based on the finite-difference time-domain method testified the experimental results.