The near-field behavior of a new plasmonic structure, the plasmonic micro-zone-plate (PMZP), is presented. The PMZP can realize superfocusing at a working distance on the micrometer scale and a resolving power beyond the diffraction limit. Compared with conventional Fresnel zone plates (CFZPs), its unique characteristics of a significantly elongated depth of focus (DOF) and focal length will make autofocusing easier for the relevant optical systems. These characteristics imply that it is possible to realize a free feedback control system for autofocusing systems in which probe scanning is performed with a constant working distance from the probe to the sample surface, provided that the flatness variation of the sample substrate is within the DOF. Moreover, unlike the CFZPs, there is no series of focal points appearing for beam propagation in the near-field region with a propagation distance ranging from λ to $8\lambda$ or even longer. In addition, transmission properties in the near-field region are investigated by means of a computational simulation based on a finite-difference time-domain numerical algorithm. Peak transmission wavelength shifts were observed while the metal film thickness was changed. Focusing characteristics were analyzed for different numerical apertures of the PMZPs.