Incorporation of nanostructured materials into the membrane matrix is a new strategy to improve mechanical and performance properties. Graphene oxide (GO) is one of the advantageous carbon-based nanomaterials, which recently has been used extensively in this field. However, in the most cases, the surface modification of GO has been considered for the creation of new properties like a response to different stimuli such as temperature, pH, and pressure. In the present study, a well-defined poly(acrylic acid) was grafted on GO using reversible addition-fragmentation chain transfer polymerization technique. This modified GO was incorporated into the mixed matrix membrane as a pH-sensitive additive and its effect on the membrane performance was investigated. The membrane with 5 wt % of modified GO provides better hydrophilicity, flux, antifouling, and rejection properties and so the effect of pH change on the aforementioned characteristic properties was studied for this membrane. It is indicated that modified membrane shows different behaviors in acidic and alkaline conditions. In addition, excellent heavy metal separation was observed among rejection tests, especially for Hg ions.