Poly(ethylene glycol) passivated graphene quantum dots (PEG-GQDs) were synthesized based on a green and effective strategy of the hydrothermal treatment of cane molasses. The prepared PEG-GQDs, with an average size of 2.5 nm, exhibit a brighter blue fluorescence and a higher quantum yield (QY) (up to approximately 21.32%) than the QY of GQDs without surface passivation (QY = 10.44%). The PEG-GQDs can be used to detect and quantify paramagnetic transition-metal ions including Fe3+, Cu2+, Co2+, Ni2+, Pb2+, and Mn2+. In the case of ethylenediaminetetraacetic acid (EDTA) solution as a masking agent, Fe3+ ions can be well selectively determined in a transition-metal ion mixture, following the lowest limit of detection (LOD) of 5.77 μM. The quenching mechanism of Fe3+ on PEG-GQDs belongs to dynamic quenching. Furthermore, Fe3+ in human serum can be successfully detected by the PEG-GQDs, indicating that the green prepared PEG-GQDs can be applied as a promising candidate for the selective detection of Fe3+ in clinics.