We report the discovery of an extended very-high-energy (VHE) gamma-ray source around the location of the middle-aged (207.8 kyr) pulsar PSR J0622+3749 with the Large High-Altitude Air Shower Observatory (LHAASO). The source is detected with a significance of 8.2σ for E>25 TeV assuming a Gaussian template. The best-fit location is (right ascension, declination) =(95.47°±0.11°,37.92°±0.09°), and the extension is 0.40°±0.07°. The energy spectrum can be described by a power-law spectrum with an index of -2.92±0.17_{stat}±0.02_{sys}. No clear extended multiwavelength counterpart of the LHAASO source has been found from the radio to sub-TeV bands. The LHAASO observations are consistent with the scenario that VHE electrons escaped from the pulsar, diffused in the interstellar medium, and scattered the interstellar radiation field. If interpreted as the pulsar halo scenario, the diffusion coefficient, inferred for electrons with median energies of ∼160 TeV, is consistent with those obtained from the extended halos around Geminga and Monogem and much smaller than that derived from cosmic ray secondaries. The LHAASO discovery of this source thus likely enriches the class of so-called pulsar halos and confirms that high-energy particles generally diffuse very slowly in the disturbed medium around pulsars.