A nearby super-luminous burst GRB 130427A was simultaneously detected by six $gamma$-ray space telescopes ({it Swift}, Fermi-GBM/LAT, Konus-Wind, SPI-ACS/INTEGRAL, AGILE and RHESSI) and by three RAPTOR full-sky persistent monitors. The isotropic $gamma-$ray energy release is of $sim 10^{54}$ erg, rendering it the most powerful explosion among the GRBs with a redshift $zleq 0.5$. 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 established for the $sim (95.3,~47.3,~41.4,~38.5,~32)$ GeV photons arriving at $tsim (243,~256.3,~610.6,~3409.8,~34366.2)$ s after the trigger of Fermi-GBM. Interestingly, the external-inverse-Compton-scattering of the prompt emission (the second episode, i.e., $tsim 120-260$ 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. Implication of the null detection of $>1$ TeV neutrinos from GRB 130427A by IceCube is discussed.
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