The molecular dynamics method was used to investigate the elastic properties of armchair and zigzag single-walled carbon nanotubes grafted by hydroxyl on their ports. The results showed that the Young's moduli of ungrafted armchair (5, 5)，(10,10) and zigzag (9, 0) , (18,0) single-walled carbon nanotubes were 948，901 and 804, 860GPa, respectively. When the single-walled carbon nanotubes were grafted by 2 to 8 hydroxyl functional groups, the Young's modulus of the zigzag single-walled carbon nanotubes was little changed, while the Young's modulus of the armchair single-walled nanotubes first decreased significantly due to the grafting, then increased appreciably to some steady value with increasing of the grafts after having been grafted to certain numbers. The reasons were analyzed in terms of the isoline structure of deformation electron density, C—C bond-length and the system binding energy variation of the carbon nanotubes with different graft numbers.