By systematically analyzing the single particle level, the single particle occupation probability near the Fermi surface, paring energy effect and the rule of nuclear particle number fluctuation of even-even nuclei of oxygen isotopes within the relativistic mean-field model with BCS theory, we compare the neutron closed shell effect of 14O,22O and 24O nuclei, and finally predict theoretically that the proton-rich 14O nucleus has stronger neutron closed shell effect than 22O and 24O nuclei.