Graphene oxide (GO) membrane has become a promising membrane due to its advantages of high flux, good anti-pollution performance, and controllable cost. Since wastewater contains inorganic ions and organic substances, the effect of inorganic ions on the removal of organic matters has attracted attention. This study investigated the impact of monovalent cations (Na+ and K+) on the removal of different organic matters by GO membranes. The results showed that the removal by GO membranes of both macromolecular organic compounds (humic acid, sodium alginate, and bull serum albumin) and small molecular organic substances (new coccine, methyl orange, and methylene blue) were high (>75%). The coexisting Na+ caused the increase in flux and the decrease in removal of small molecular organic matters, while the impact on the removal of macromolecular organic matters was weak. The impact of the coexisting K+ was weaker than Na+. With the crosslinking of ethylenediamine, the structure of GO membrane was more stable. The impacts of Na+ on the flux and separation performance of crosslinked membranes were less than that of non-crosslinked membranes. This suggests that crosslinked GO membrane has more potential for practical wastewater treatment.