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In this work, we calculate the fragmentation function (FF) of gluon splitting into the quarkonium bound state at next-to-leading order perturbative QCD. To this end, we apply the well-established Suzuki's model which is convenient to consider the polarization states of produced quarkonium. To be specific, we restrict ourselves to the fragmentation of gluon into the S-wave pseudoscalar mesons ηc and ηb. We will compare our results with the one computed at the leading-order (LO) to show the effects of higher order radiative corrections. Our results show that the NLO radiative corrections may improve the LO FFs up to 70%, so this shows the importance of NLO corrections.