A blazar Mrk 501, suddenly came into a very active phase from February
in 1997, with several large flares and lasted for almost half a year.
The maximum gamma-ray flux during this period reached about 10 times
as high as the Crab Nebula. Using the data obtained with a Tibet HD
Air Shower Array, we searched for gamma-ray signals from Mrk 501
during the period from February 15 to August 25 in 1997. We found
our array detected multi-TeV gamma rays from this source with 3.7 $B&R(B
level. The most rapid increase of the excess count of air shower
events was observed between April 7 and June 16 and the statistical
significance of the excess counts in this 70 days was 4.7 $B&R(B.
According to a simulation using the angular resolution of our
array, the distribution of arrival direction of air shower events
is consistent with gamma-ray initiated air showers coming from the
point source. The average flux of gamma rays from Mrk 501 is estimated
as 4.50($B!^(B1.20) $B!_(B 10-12 cm-2s-1
TeV-1 for energy above 3 TeV in the period from February
15 to August 25, and 9.09($B!^(B1.52) $B!_(B
TeV-1 in the period from April 7 to June 16. This
is a first detection of extragalactic gamma-ray source by conventional
surface array. The observed gamma-ray energy spectrum suggests to be
somewhat suffered from an absorption in the energy region above 6 TeV
by intergalactic infrared photons.