Fully epitaxial magnetic tunnel junctions (MTJs) were fabricated with a full-Heusler alloy Co2Cr0.6Fe0.4Al (CCFA) thin film and a MgO tunnel barrier. Pseudo-spin-valve-type, fully epitaxial CCFA/MgO/Co50Fe50 MTJs with a CCFA film composition close to the stoichiometric one demonstrated high tunnel magnetoresistance (TMR) ratios of 90% at room temperature (RT) and 240% at 4.2K. These high TMR ratios were attributed to the increased spin polarization at the Fermi level due to the increased ratio of the B2 region to the A2 region in CCFA films achieved by bringing the CCFA film composition close to the stoichiometric one. Fully epitaxial CCFA/MgO/Co50Fe50 MTJs with exchange biasing were also fabricated, where a Co50Fe50 upper electrode was used in a synthetic ferrimagnetic Co50Fe50/Ru/Co90Fe10 trilayer exchange-biased with an IrMn layer through the Co90Fe10/IrMn interface. These exchange-biased CCFA/MgO/Co50Fe50 MTJs exhibited further enhanced TMR ratios of 109% at RT and 317% at 4.2K. We suggested enhancement of the TMR ratio by a coherent tunneling contribution for fully epitaxial - CCFA/MgO/Co50Fe50 MTJs.