The unbound excited states of the neutron drip-line isotope 24O have been investigated via the 24O(p,p')23O + n reaction in inverse kinematics at a beam energy of 62 MeV/nucleon. The decay energy spectrum of 24O* was reconstructed from the momenta of 23O 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(π) = 2+ from the angular distribution of the cross section. Higher-lying states were also observed. The quadrupole transition parameter β2 of the 2(1)+ state was deduced, for the first time, to be 0.15±0.04. The relatively high excitation energy and small β2 value are indicative of the N = 16 shell closure in 24O.