A sub-array of the Large High Altitude Air Shower Observatory (LHAASO), KM2A is mainly designed to observe a large fraction of the northern sky to hunt for γ-ray sources at energies above 10 TeV. Even though the detector construction is still underway, half of the KM2A array has been operating stably since the end of 2019. In this paper, we present the KM2A data analysis pipeline and the first observation of the Crab Nebula, a standard candle in very high energy γ-ray astronomy. We detect γ-ray signals from the Crab Nebula in both energy ranges of 10 100 TeV and 100 TeV with high significance, by analyzing the KM2A data of 136 live days between December 2019 and May 2020. With the observations, we test the detector performance, including angular resolution, pointing accuracy and cosmic-ray background rejection power. The energy spectrum of the Crab Nebula in the energy range 10-250 TeV fits well with a single power-law function dN/dE = (1.13 0.05 0.08 ) 10 (E/20 TeV) cm s TeV . It is consistent with previous measurements by other experiments. This opens a new window of γ-ray astronomy above 0.1 PeV through which new ultrahigh-energy γ-ray phenomena, such as cosmic PeVatrons, might be discovered.