Epitaxial discontinuous Fe/MgO multilayers have been grown by pulsed laser deposition on MgO(001) single-crystal substrates. The multilayers with 0.6 nm nominal Fe layers thickness are superparamagnetic and demonstrate tunneling magnetoresistance (TMR) in the current-in-plane configuration. Increasing deposition temperature causes an improvement in crystal quality and is accompanied by higher TMR ratios. The maximum value (9.2% TMR at room temperature and 18 kOe magnetic field) trebles that of polycrystalline samples deposited simultaneously on glass substrates. A model formula for TMR ratio that includes both spin-dependent tunneling and spin-filtering effect is proposed to explain these results.