The ARGO-YBJ experiment is a full-coverage air shower detector located at the Yangbajing Cosmic Ray Observatory (Tibet, People's Republic of China, 4300 m a.s.l.). The high altitude, combined with the full-coverage technique, allows the detection of extensive air showers in a wide energy range and offer the possibility of measuring the cosmic ray proton plus helium spectrum down to the TeV region, where direct balloon/space-borne measurements are available. The detector has been in stable data taking in its full configuration from November 2007 to February 2013. In this paper the measurement of the cosmic ray proton plus helium energy spectrum is presented in the region 3-300 TeV by analyzing the full collected data sample. The resulting spectral index is gamma = -2.64 +/- 0.01, the error is dominated by systematic uncertainties. The accurate measurement of the spectrum of light elements with a ground based air shower detector demonstrates the possibility of extending these measurements at larger energies, where galactic cosmic ray sources should run out of power in accelerating light elements.