We report large tunnel magnetoresistance (TMR) ratios of up to 219% at 300 K and 366% at 3.7 K obtained for a high-quality fully epitaxial double-barrier magnetic tunnel junction (MTJ) composed of Fe/MgO/Fe/γ-Al2O3/Nb-doped SrTiO3. The obtained TMR ratios are among the highest values reported in Fe/MgO/Fe structures. This result may be attributed to the small in-plane wave vectors of the tunneling electrons injected from the Nb-doped SrTiO3 electrode with a small carrier density, demonstrating good compatibility between the Fe-based MTJ and SrTiO3.