Membrane biofouling has inhibited permselective separation processes for decades, requiring frequent membrane backwash treatment or replacement to maintain efficacy. However, frequent treatment is not viable for devices with a continuous blood flow such as a wearable or implantable dialyzer. In this study, the biofouling characteristics of a highly hemocompatible graphene oxide (GO) membrane developed through a novel self-assembly process is studied in a protein-rich environment and compared with performance of a state-of-the-art commercial polymer membrane dialyzer. The studies are conducted in phosphate-buffered saline (PBS) environment using human serum albumin (HSA), which represents 60% of the blood protein, at the nominal blood protein concentration of 1 g L-1. Protein aggregation on the membrane surface is evaluated by monitoring the change in the membrane flux and SEM imaging. The GO membrane water flux declined only ~10% over a week-long test whereas the polymer membrane flux declined by 50% during the same period. The SEM images show that HSA primarily aggerates over the graphitic regions of nanoplatelets, away from the charged hydrophilic edges. This phenomenon leaves the open areas of the membrane formed between the nanoplatelets edges, through which the species pass, relatively intact. In contrast, HSA completely plugs the polymer membrane pores resulting in a steady decline in membrane permeability.