The Crab Nebula is a steady radiation source, which has been used as a reference source in very high energy $\gamma$-ray astronomy for calibration and verification of detectors, however the $\gamma$-ray flares around GeV from the Crab Nebula have been observed many times by AGILE and Fermi-LAT. These observations challenge the standard models for particle acceleration in pulsar wind nebula. One square kilometer detector array (KM2A) of the Large High Altitude Air Shower Observatory (LHAASO) is designed to detect $\gamma$-ray sources with high sensitivity at 100 TeV. In this work, half of the KM2A detector performance, the observations of the Crab Nebula in the energy range above 10 TeV and the results of searching for $\gamma$-ray flares will be presented using data collected with half of the KM2A and three-quarter KM2A.