The extended TeV gamma-ray source ARGO J2031+4157 (or MGRO J2031+41) is positionally consistent with the Cygnus Cocoon discovered by Fermi-LAT at GeV energies in the Cygnus superbubble. Reanalyzing the ARGO-YBJ data collected from 2007 November to 2013 January, the angular extension and energy spectrum of ARGO J2031+4157 are evaluated. After subtracting the contribution of the overlapping TeV sources, the ARGO-YBJ excess map is fitted with a two-dimensional Gaussian function in a square region of 10degrees x 10degrees, finding a source extension sigma sub(ext)= 1degrees.8 + or - 0degrees.5. The observed differential energy spectrum is dN/dE = (2.5 + or - 0.4) x 10 super(-11) (E/1 TeV) super(-2.6+ or -0.3) photons cm super(-2) s super(-1) TeV super(-1), in the energy range 0.2-10 TeV. The angular extension is consistent with that of the Cygnus Cocoon as measured by Fermi-LAT and the spectrum also shows a good connection with the one measured in the 1-100 GeV energy range. These features suggest to identify ARGO J2031+4157 as the counterpart of the Cygnus Cocoon at TeV energies. The Cygnus Cocoon, located in the star-forming region of Cygnus X, is interpreted as a cocoon of freshly accelerated cosmic rays related to the Cygnus superbubble. The spectral similarity with supernova remnants (SNRs) indicates that the particle acceleration inside a superbubble is similar to that in an SNR. The spectral measurements from 1 GeV to 10 TeV allows for the first time to determine the possible spectrum slope of the underlying particle distribution. A hadronic model is adopted to explain the spectral energy distribution.