We have observed the blazar Markarian 421 (z=0.031 ) with the TACTIC gamma- ray telescope having thresholdenergy of 1.5TeV at Mt. Abu Rajasthan India from January to April 2004. Observations were made intracking mode for a total of 84(on) /16 (off-source) hours with its imaging element equipped with a 349- pixelPMTs camera. During this period, we nd an evidence of a TeV gamma-ray signal with a statistical signi-cance of 6.8. The differential energy spectrum derived in the energy range 2 - 9 TeV is well represented bya simple power law, with a differential spectral index of 2.800.20.