A circularly polarized vortex beam possesses similar focusing properties as a radially polarized beam. This type of beam is highly valuable for developing optical manufacturing technology, microscopy, and particle manipulation. In this work, a left-hand circularly polarized terahertz (THz) vortex beam (CPTVB) is generated by utilizing a THz quarter wave plate and a spiral phase plate. Focusing properties of its longitudinal component Ez are detailedly discussed on the simulation and experiment. With reducing the F-number of the THz beam and comparing with a transverse component Ex of a general circularly polarized THz beam, the simulation results show that the focal spot size and intensity of its Ez component can reach 87 and 50% of Ex under a same focusing condition. In addition, the experimental results still demonstrate that the left-hand CPTVB can always maintain fine Ez focusing properties in a broad bandwidth, which manifest the feasibility of this class of THz beams.