A magnetic tunnel junction with a perpendicular magnetic easy-axis (p-MTJ) is a key device for spintronic non-volatile magnetoresistive random access memory (MRAM). Co-Fe-B alloy-based p-MTJs are being developed, although they have a large magnetisation and medium perpendicular magnetic anisotropy (PMA), which make it difficult to apply them to a future dense MRAM. Here, we demonstrate a p-MTJ with an epitaxially strained MnGa nanolayer grown on a unique CoGa buffer material, which exhibits a large PMA of more than 5 Merg/cm(3) and magnetisation below 500 emu/cm(3); these properties are sufficient for application to advanced MRAM. Although the experimental tunnel magnetoresistance (TMR) ratio is still low, first principles calculations confirm that the strain-induced crystal lattice distortion modifies the band dispersion along the tetragonal c-axis into the fully spin-polarised state; thus, a huge TMR effect can be generated in this p-MTJ.