A nearby superluminous burst GRB 130427A was simultaneously detected by six γ-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 γ-ray energy release is ∼1054 erg, rendering it the most powerful explosion among gamma-ray bursts (GRBs) with a redshift z ⩽ 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 γ-rays at energies above 10 GeV, while five were detected in the same time interval. A possible unified model for the prompt soft γ-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.