  We prove the Hasse principle for a smooth proper model of a geometrically
integral non-conical intersection of two quadrics in the projective space of
dimension 7 over a number field. This result generalizes the result of
Heath-Brown who established the statement in the smooth case. Our argument is
built upon the ideas of Colliot-Th\'el\`ene and the fibration method for
zero-cycles in the form of Harpaz-Wittenberg.
