Based on 42 months of observations by the Large High Altitude Air Shower Observatory(LHAASO), we report on the active behavior of the blazar Mrk 501, which exhibited several high states during this period. The most dramatic flare occurred between MJD 59334 and MJD 59348, reaching 62% of the Crab Nebula flux (> 1 TeV). The global spectral energy distribution (SED) of Mrk 501 above 1 TeV is well described by a power-law model with an exponential cutoff, yielding a power-law index of 𝛼 = 2.18 ± 0.04 and a cutoff energy of 𝐸cut = 9.51 ± 1.44 TeV. Ongoing studies focus on multi-wavelength correlations and broadband spectral modeling to further understand the underlying physical mechanisms driving these phenomena. LHAASO's all-weather capability and high duty cycle provide critical continuous data for such investigations.