Plasmonic lens (PL) is a nano-optical device, with which a tight focusing spot in a subwavelength-scale can be achieved by exciting and controlling surface plasmon polaritons (SPPs), thus the diffraction limit can be broken for attaining the shorter effective wavelength of the SPPs. The key issue in studying the PL is to achieve a tight focusing point and focus-control effectively. Optimal plasmonic focusing can be achieved by utilizing the radially polarized light and the rotational symmetric structures of the PL. Radially polarized light is a cylindrical vector beam whose local polarization of electric field is always parallel to the radial direction. As a radially polarized light is used as the incident light in a PL, the SPPs can be excited in all directions, so as to increase the efficiency of focussing. The focussing efficiency can be further increased, and the characteristics of the focus, such as spot size, shape, and strength etc., can be manipulated through appropriate designs of the PL structures. In this work, under an illumination of a radially polarized light, a new type of plasmonic lens is proposed to achieve a long depth of focus (DOF), a long focal length, and a sub-wavelength-scale tight focussing spot. This kind of plasmonic lens consists of a T-shape micro-hole, concentric rings, and multi-level step-like structures. The focussing properties of such plasmonic lenses are analyzed in terms of the finite element method (FEM). Simulation results show that SPPs can be excited efficiently in such structures and the tight-focusing is realized via the multiple-beam interference between the light radiating from the concentric rings and the transmitted light from the center hole. The T-shape micro-hole and step-like concentric ring structures can provide control for the phase modulation and the propagation direction of the SPPs along the bottom of the groove, thus leading to a compressed focal spot, a longer focal length, an increased depth of focus, and to improving the focussing properties. In an optimized PL design, a focal spot of ～2.5λ0 DOF, ～0.388λ0 FWHM, and ～3.22λ0 focal length is achieved under the illumination of a radially polarized light (λ0=632.8 nm). The PL structure is compact, and can be easily integrated with other nano-devices. The PL proposed above has potential applications in nano-scale photonic integration, near-field imaging and sensing, nano-photolithography, and in other related areas.