We present the active galactic nuclei (AGN) catalog from the fourth data release (HDR4) of the Hobby-Eberly Telescope Dark Energy Experiment Survey (HETDEX). HETDEX is an untargeted spectroscopic survey. HDR4 contains 345,874 Integral Field Unit observations from 2017 January to 2023 August covering an effective area of 62.9deg2. With no imaging preselection, our spectroscopic confirmed AGN sample includes low-luminosity AGN, narrow-line AGN, and/or red AGN down to g~25. This catalog has 15,940 AGN across the redshifts of z=0.1~4.6, giving a raw AGN number density of 253.4deg^-2^. Among them, 10,499 (66%) have redshifts either confirmed by line pairs or matched to the Sloan Digital Sky Survey Quasar Catalog. For the remaining 5441 AGN, 2083 are single broad-line AGN candidates, while the remaining 3358 are single intermediate broad-line (full width at half-maximum, FWHM~1200km/s) AGN candidates. A total of 4060 (39%) of the 10,499 redshift-confirmed AGN have emission-line regions 3{sigma} more extended than the image quality, which could be strong outflows blowing into the outskirts of the host galaxies or ionized intergalactic medium.