  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 $8.2\sigma$ for $E>25$~TeV assuming a Gaussian
template. The best-fit location is (R.A.,
Dec.)$=(95^{\circ}\!.47\pm0^{\circ}\!.11,\,37^{\circ}\!.92 \pm0^{\circ}\!.09)$,
and the extension is $0^{\circ}\!.40\pm0^{\circ}\!.07$. The energy spectrum can
be described by a power-law spectrum with an index of ${-2.92 \pm 0.17_{\rm
stat} \pm 0.02_{\rm sys} }$. No clear extended multi-wavelength 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 $\sim160$~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.
