A novel energy reconstruction procedure based on the utilization of Articial Neural Network has been developedfor the TACTIC atmospheric Cerenkov imaging telescope to estimate the energy of the primary gammaraysin the TeV energy range. The procedure uses a 3:20:1 conguration of the ANN with resilient backpropagationtraining algorithm to estimate the energy of a-ray like event on the basis of its image SIZE,DISTANCE and zenith angle. The results obtained by using the CORSIKA code simulated data suggest theenergy resolution of the telescope is40for retaining90of the-ray events in a particular energybin which is comparable to the energy resolution of other single element imaging telescopes. Details of theenergy estimation procedure along with results obtained by determining the Crab Nebula energy spectrum inthe energy range 1-16 TeV as measured by the TACTIC telescope are presented in the paper.