We report on the discovery of high-energy ( HE ; E > 0.1 GeV ) and very high-energy ( VHE ; E > 100 GeV ) \gamma -ray emission from the high-frequency-peaked BL Lac object RBS 0413 . VERITAS , a ground-based \gamma -ray observatory , detected VHE \gamma rays from RBS 0413 with a statistical significance of 5.5 standard deviations ( \sigma ) and a \gamma -ray flux of ( 1.5 \pm 0.6 _ { \mathrm { stat } } \pm 0.7 _ { \mathrm { syst } } ) \times 10 ^ { -8 } photons \textrm { m } ^ { -2 } \textrm { s } ^ { -1 } ( \sim 1 \% of the Crab Nebula flux ) above 250 GeV . The observed spectrum can be described by a power law with a photon index of 3.18 \pm 0.68 _ { \mathrm { stat } } \pm 0.30 _ { \mathrm { syst } } . Contemporaneous observations with the Large Area Telescope ( LAT ) on the Fermi Gamma-ray Space Telescope detected HE \gamma rays from RBS 0413 with a statistical significance of more than 9 \sigma , a power-law photon index of 1.57 \pm { 0.12 _ { \mathrm { stat } } } ^ { +0.11 } _ { -0.12 \mathrm { sys } } and a \gamma -ray flux between 300 MeV and 300 GeV of ( 1.64 \pm { 0.43 _ { \mathrm { stat } } } ^ { +0.31 } _ { -0.22 \mathrm { sys } } ) \times 10 ^ { -5 } photons m ^ { -2 } s ^ { -1 } . We present the results from Fermi -LAT and VERITAS , including a spectral energy distribution modeling of the \gamma -ray , quasi-simultaneous X-ray ( Swift -XRT ) , ultraviolet ( Swift -UVOT ) and R -band optical ( MDM ) data . We find that , if conditions close to equipartition are required , both the combined synchrotron self-Compton/external-Compton and the lepto-hadronic models are preferred over a pure synchrotron self-Compton model .