We extend the concept of spiral zone plates along the optical axis and define a specific single optical element, termed as single-focus spiral zone plates (SFSZPs), for the generation of a single-focus vortex beam. The key idea is to make the transmittance of the spiral zone plates sinusoidal in the azimuthal direction. Furthermore, a two-parameter modified sinusoidal apodization window is introduced to modulate the transmittance function. Theoretical analysis reveals that the third-order diffraction light intensity of the SFSZPs could be reduced by more than three orders of magnitude compared to a conventional spiral zone plate. The experimental results are also presented, confirming the desired single-focus characteristics. The unique single-focus phase singularity properties imply that SFSZPs may find a wide range of imaging and microscopy applications, as well as fundamental studies of vortex beams.