We report the discovery of a new unidentified extended gamma-ray source in the Galactic plane named LHAASO J0341+5258 with a pretrial significance of 8.2 standard deviations above 25 TeV. The best-fit position is R.A. = 55.degrees 34 +/- 0.degrees 11 and decl. = 52.degrees 97 +/- 0.degrees 07. The angular size of LHAASO J0341+5258 is 0.degrees 29 +/- 0.degrees 06(stat) +/- 0.degrees 02(sys). The flux above 25 TeV is about 20% of the flux of the Crab Nebula. Although a power-law fit of the spectrum from 10 to 200 TeV with the photon index alpha = 2.98 +/- 0.19(stat) +/- 0.02(sys) is not excluded, the LHAASO data together with the flux upper limit at 10 GeV set by the Fermi-LAT observation, indicate a noticeable steepening of an initially hard power-law spectrum with a cutoff at approximate to 50 TeV. We briefly discuss the origin of ultra-high-energy gamma rays. The lack of an energetic pulsar and a young supernova remnant inside or in the vicinity of LHAASO J0341+5258 challenge, but do not exclude, both the leptonic and hadronic scenarios of gamma-ray production.