  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.
