The focusing characteristics of Fresnel zone plate (FZP) on vortex beams at 1550 nm are investigated. Employing the Fresnel diffraction integral, the diffraction characteristics on different circular structures are calculated. Many calculations and measurements of the transmission light field-phase distribution demonstrate that the focusing characteristics of the vortex beam through FZP are similar to Gaussian beam. The effect of radius-dependent phase delay on the focus position is verified. At the same time, it is proved that the topological charge has nothing to do with the major focal position and the FZP will not change the topological charge of the incident vortex beam.