We report the detection of an extended very-high-energy(VHE) γ-ray source coincident with the location of middle-aged(62.4 kyr) pulsar PSR J0248+6021,by using the LHAASO-WCDA data of live 796 d and LHAASO-KM2A data of live 1216d.A significant excess of y-ray induced showers is observed both by WCDA in energy bands of 1-25 TeV and KM2A in energy bands of25 TeV with 7.3σ and 13.5σ,respectively.The best-fit position derived through WCDA data is R.A.=42.06°±0.12°and Dec.=60.24°±0.13° with an extension of 0.69°±0.15° and that of the KM2A data is R.A.=42.29°±0.13° and Dec.=60.38°±0.07° with an extension of 0.37°±0.07°.No clear extended multiwavelength counterpart of this LHAASO source has been found from the radio band to the GeV band.The most plausible explanation of the VHE γ-ray emission is the inverse Compton process of highly relativistic electrons and positrons injected by the pulsar.These electrons/positrons are hypothesized to be either confined within the pulsar wind nebula or to have already escaped into the interstellar medium,forming a pulsar halo.