We have observed the blazar Markarian 421 with the TACTIC γ -ray telescope at Mt. Abu, India, from 22 November 2009 to 16 May 2010 for 265 h. Detailed analysis of the data so recorded revealed the presence of a TeV γ -ray signal with a statistical significance of 12.12σ at Eγ ≥1 TeV. We have estimated the time-averaged differential energy spectrum of the source in the energy range 1.0–16.44 TeV. The spectrum fits well with the power-law function of the form (dF/dE = f₀E^−Γ) with f₀ = (1.39 ± 0.239) × 10⁻¹¹ cm⁻² s⁻¹ TeV⁻¹ and Γ = 2.31 ± 0.14.