As one of the brightest active blazars in both X-ray and very high energy $gamma$-ray bands, Mrk 501 is very useful for physics associated with jets from AGNs. The ARGO-YBJ experiment is monitoring it for $gamma$-rays above 0.3 TeV since November 2007. Starting from October 2011 the largest flare since 2005 is observed, which lasts to about April 2012. In this paper, a detailed analysis is reported. During the brightest $gamma$-rays flaring episodes from October 17 to November 22, 2011, an excess of the event rate over 6 $sigma$ is detected by ARGO-YBJ in the direction of Mrk 501, corresponding to an increase of the $gamma$-ray flux above 1 TeV by a factor of 6.6$pm$2.2 from its steady emission. In particular, the $gamma$-ray flux above 8 TeV is detected with a significance better than 4 $sigma$. Based on time-dependent synchrotron self-Compton (SSC) processes, the broad-band energy spectrum is interpreted as the emission from an electron energy distribution parameterized with a single power-law function with an exponential cutoff at its high energy end. The average spectral energy distribution for the steady emission is well described by this simple one-zone SSC model. However, the detection of $gamma$-rays above 8 TeV during the flare challenges this model due to the hardness of the spectra. Correlations between X-rays and $gamma$-rays are also investigated.
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