The rare-earth compounds R2O2Bi (R = Tb, Dy, Er, Lu, Y) are newly discovered superconductors in the vicinity of a rare-earth magnetic long-range order. In this work, we determined the magnetic order of the parent compound Dy2O2Te by neutron scattering as the A-type antiferromagnetic structure below the Néel temperature TN = 9.7 K. The large staggered magnetic moment 9.4(1)µB per Dy at T = 3.5 K lies in the basal ab-plane. In a magnetic field, anomalous magnetic properties including the bifurcation between zero-field and field cooling magnetization, a butterfly-shaped magnetic hysteresis and slow magnetic relaxation emerge, which are related to the field-induced metamagnetic transitions in Dy2O2Te. Our experimental findings would stimulate further research on the relation between antiferromagnetism and superconductivity in these rare-earth compounds.