The maximum mass of neutron stars (NSs) is of great importance for constraining equations of state of NSs and understanding the mass gap between NSs and stellar-mass black holes. NSs in X-ray binaries would increase in mass by accreting material from their companions (known as recycling process), and the uncertainties in the accretion process give challenge to study the NS mass at birth. {In this work, we investigate the NS accreted mass with considering the effect of NS spin evolution and give the maximum accreted mass for NSs in the recycling process. By exploring a series of binary evolution calculations, we obtain the final NS mass and the maximum accreted mass for a given birth mass of NS and a mass transfer efficiency. Our results show that the NSs can accrete relatively more material for binary systems with the donor masses in the range of $1.8sim 2.4M_odot$, the NSs accrete relatively more mass when the remnant WD mass is in the range of $sim 0.25-0.30M_odot$, and the maximum accreted mass is positively correlated with the initial NS mass. For a $1.4M_odot$ NS at birth with a moderate mass transfer efficiency of 0.3, the maximum accreted mass could be $0.27M_odot$. The results can be used to estimate the minimum birth mass for systems with massive NSs in observations.
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