This study aims to investigate the process of terahertz wave generation using a vortex beam generated by spatial light modulator rather than a Gaussian beam as the light source. Herein, we explore the differences among vortex beams with different topological charge numbers when generating terahertz waves. We find that the generation of terahertz waves is affected by the phase singularity position. In addition, we investigate the changes of terahertz wave energy, spectrum, and polarization produced by vortex beams with different pulse intensities and laser wavelengths. The results demonstrate that the intensity of the terahertz wave changes with the topological charge number, which is also closely related to the position of the vortex center. Under the same vortex beam, the variation of the generated terahertz wave with pulse intensity and laser wavelength is consistent with that for a Gaussian beam. Specifically, the terahertz waves generated by a vortex beam and a Gaussian beam are consistent in terms of spectrum and polarization.