The High-Energy Telescope (HET) for the EPI-Hi instrument on Parker Solar Probe (PSP) is designed to measure solar energetic-particle (SEP), interplanetary, and galactic cosmic-ray (CGR) ions with 1≤Z≤30 from ~10 MeV/nuc to several hundred MeV/nuc, and electrons from ~0.5 to ~8 MeV. HET also includes a ‘neutral-particle’ coincidence mode designed to assess the fraction of electron-like events due to g-rays that Compton scatter or pair-produce in the telescope. Based on g-rayobservationsby SMM, RHESSI and Fermi, along with laboratory calibrations with radioactive g-ray sources, we believe HET is capable of detecting solar g-ray flares, especially when PSP is close to the Sun. This paperillustrateshow HET detects solar g-rays and presents “quiet-time background” g-ray spectra (due mainly to g-rays produced by cosmic-ray interactions in surrounding spacecraft material).The estimated g-ray yield from the October 28, 2003 events is used as an example of the HET sensitivity.