Optical vortices (OVs) with orbital angular momenta show promise for various optical applications. Spiral zone plates (SZPs) can generate a focused OV and are thus used in applications like edge-enhanced imaging. However, conventional SZPs have low diffraction efficiency because they operate based on amplitude modulation. This study proposes a liquid crystal spiral zone plate (LCSZP) that operates based on phase modulation and demonstrates the generation of a focused OV with high efficiency and electric tunability. The LCSZP has no threshold voltage owing to its homeotropic/planar hybrid alignment regions, and it can find applications in imaging, laser processing, and optical manipulation.