We have observed Markarian 501 in Very High Energy (VHE) gamma-ray wavelength band for 70.6 h from 15 April to 30 May, 2012 using TACTIC telescope. Detailed analysis of ∼66.3 h of clean data revealed the presence of a TeV γ-ray signal (686 ±77 γ-ray events) from the source direction with a statistical significance of 8.89σ above 850 GeV. Further, a total of 375 ±47 γ-ray like events were detected in 25.2 h of observation from 22 –27 May, 2012 with a statistical significance of 8.05 σ indicating that the source has possibly switched over to a relatively high gamma-ray emission state. We have derived time- averaged differential energy spectrum of the state in the energy range 850 GeV- 17.24 TeV which fits well with a power law function of the form dF/dE = f₀ E^−Γ with  f ₀ = (2 . 27 ±0 . 38) ×10⁻¹¹ photons cm⁻²s⁻¹ TeV⁻¹ and Γ= 2.57±0.15. In order to investigate the source state, we have also used almost simultaneous multiwave length observations viz: high energy data collected by Fermi-LAT, X-ray data collected by Swift -XRT and MAXI, optical and UV data collected by Swift -UVOT, and radio data collected by OVRO, and reconstructed broad-band Spectral Energy Distribution (SED). The obtained SED supports leptonic model (homogeneous single zone) for VHE gamma-ray emission involving synchrotron and synchrotron self Compton (SSC) processes.