We present both numerical and experimental results to study the diffraction of twisted light beams based on orbital angular momentum (OAM) eigenmode decomposition, where the total initial field, including light and aperture, is represented by a two-dimensional spectrum of Laguerre–Gaussian modes. We use a phase-only spatial light modulator to display a holographic grating for both generating the twisted light and mimicking the finite aperture. We take a triangular aperture as an example to describe the diffraction behavior of a twisted light beam carrying an OAM number of =3 from the near-field to far-field regions, where the interesting gradual formation of triangular bright lattices are observed. An excellent agreement between the numerical simulations and experimental observations is clearly seen. It is noted that this method is particularly useful for the study of the diffraction of twisted light fields incident on any apertures of rotational symmetry.