Using magnetization, dielectric constant, and neutron diffraction measurements on a high quality single crystal of YBaCuFeO5 (YBCFO), we demonstrate that the crystal shows two antiferromagnetic transitions at [Formula: see text] K and [Formula: see text] K, and displays a giant dielectric constant with a characteristic of the dielectric relaxation at T N2. It does not show the evidence of the electric polarization for the crystal used for this study. The transition at T N1 corresponds with a paramagnetic to antiferromagnetic transition with a magnetic propagation vector doubling the unit cell along three crystallographic axes. Upon cooling, at T N2, the commensurate spin ordering transforms to a spiral magnetic structure with a propagation vector of ([Formula: see text] [Formula: see text] [Formula: see text]), where [Formula: see text], [Formula: see text], and [Formula: see text] are odd, and the incommensurability δ is temperature dependent. Around the transition boundary at T N2, both commensurate and incommensurate spin ordering coexist.