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We investigated the spin-dependent transport properties of Fe/MgAl2O4/Fe(001) magnetic tunneling junctions (MTJs) on the basis of first-principles calculations of the electronic structures and the ballistic conductance. The calculated tunneling magnetoresistance (TMR) ratio of a Fe/MgAl2O4/Fe(001) MTJ was about 160%, which was much smaller than that of a Fe/MgO/Fe(001) MTJ (1600%) for the same barrier thickness. However, there was an evanescent state with ∆1 symmetry in the energy gap around the Fermi level of normal spinel MgAl2O4, indicating the possibility of a large TMR in Fe/MgAl2O4/Fe(001) MTJs. The small TMR ratio of the Fe/MgAl2O4/Fe(001) MTJ was due to new conductive channels in the minority spin states resulting from a band-folding effect in the two-dimensional (2-D) Brillouin zone of the in-plane wave vector (k ) of the Fe electrode. Since the in-plane cell size of MgAl2O4 is twice that of the primitive in-plane cell size of bcc Fe, the bands in the boundary edges are folded, and minority-spin states coupled with the ∆1 evanescent state in the MgAl2O4 barrier appear at k =0, which reduces the TMR ratio of the MTJs significantly.