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We present the first Active Galactic Nuclei (AGN) catalog in the Hobby-Eberly Telescope Dark Energy Experiment Survey (HETDEX) observed between January 2017 and June 2020. HETDEX is an ongoing spectroscopic survey with no pre-selection based on magnitudes, colors or morphologies, enabling us to select AGN based on their spectral features. Both luminous quasars and low-luminosity Seyferts are found in our catalog. AGN candidates are selected with at least two significant AGN emission lines, such as the LyA and CIV line pair, or with single broad emission lines (FWHM > 1000 km/s). Each source is further confirmed by visual inspections. This catalog contains 5,322 AGN, covering an effective sky coverage of 30.61 deg^2. A total of 3,733 of these AGN have secure redshifts, and we provide redshift estimates for the remaining 1,589 single broad-line AGN with no cross matched spectral redshifts from SDSS DR14Q. The redshift range of the AGN catalog is 0.25 < z < 4.32, with a median of z = 2.1. The bolometric luminosity range is 10^9-10^14 Lsun with a median of 10^12 Lsun. The median r-band magnitude of the AGN is 21.6 mag, with 34% of the AGN have r > 22.5, and 2.6% reaching the detection limit at r ~ 26 mag of the deepest imaging surveys we searched. We also provide a composite spectrum of the AGN sample covering 700 AA - 4400 AA.