The Crab Nebula has been observed by the HEGRA (High-Energy Gamma-Ray Astronomy) stereoscopic system of imaging air Cerenkov telescopes (IACTs) for a total of ~200 hr during two observational campaigns: from 1997 September to 1998 March and from 1998 August to 1999 April. The recent detailed studies of system performance give an energy threshold and an energy resolution for γ-rays of 500 GeV and ~18%, respectively. The Crab energy spectrum was measured with the HEGRA IACT system in a very broad energy range up to 20 TeV, using observations at zenith angles up to 65°. The Crab data can be fitted in the energy range from 1 to 20 TeV by a simple power law, which yields dJγ/dE=(2.79+/-0.02+/- 0.5)×10-7(E/1 TeV)-2.59+/-0.03+/-0.05 photons m-2 s-1 TeV-1. The Crab Nebula energy spectrum, as measured with the HEGRA IACT system, agrees within 15% in the absolute scale and within 0.1 units in the power-law index with the latest measurements by the Whipple, CANGAROO, and CAT groups, consistent within the statistical and systematic errors quoted by the experiments. The pure power-law spectrum of TeV γ-rays from the Crab Nebula constrains the physics parameters of the nebula environment as well as the models of photon emission.