The unbound excited states of the neutron drip-line isotope O-24 have been investigated via the O-24(p, p')O-23 + n reaction in inverse kinematics at a beam energy of 62 MeV/nucleon. The decay energy spectrum of O-24* was reconstructed from the momenta of O-23 and the neutron. The spin parity of the first excited state, observed at E-x = 4.65 +/- 0.14 MeV, was determined to be J(pi) = 2(+) from the angular distribution of the cross section. Higher-lying states were also observed. The quadrupole transition parameter beta(2) of the 2(1)(+) state was deduced, for the first time, to be 0.15 +/- 0.04. The relatively high excitation energy and small beta(2) value are indicative of the N = 16 shell closure in O-24.