A nearby superluminous burst GRB 130427A was simultaneously detected by six gamma -ray space telescopes (Swift, the Fermi GLAST Burst Monitor (GBM)/Large Area Telescope, Konus-Wind, SPI-ACS/INTEGRAL, AGILE, and RHESSI) and by three RAPTOR full-sky persistent monitors. The isotropic gamma -ray energy release is ~10 super(54) erg, rendering it the most powerful explosion among gamma-ray bursts (GRBs) with a redshift z < or =, slant 0.5. The emission above 100 MeV lasted about one day, and four photons are at energies greater than 40 GeV. We show that the count rate of 100 MeV-100 GeV emission may be mainly accounted for by the forward shock synchrotron radiation and the inverse Compton radiation likely dominates at GeV-TeV energies. In particular, an inverse Compton radiation origin is favored for the ~(95.3, 47.3, 41.4, 38.5, 32) GeV photons arriving at t ~ (243, 256.3, 610.6, 3409.8, 34366.2) s after the trigger of Fermi-GBM. Interestingly, the external inverse Compton scattering of the prompt emission (the second episode, i.e., t ~ 120-260 s) by the forward-shock-accelerated electrons is expected to produce a few gamma -rays at energies above 10 GeV, while five were detected in the same time interval. A possible unified model for the prompt soft gamma -ray, optical, and GeV emission of GRB 130427A, GRB 080319B, and GRB 090902B is outlined. Implications of the null detection of > 1 TeV neutrinos from GRB 130427A by IceCube are discussed.