Few (macro)molecular inhibitors of inorganic scale can suppress both nucleation and crystal growth. In this study, we examine a series of potential inhibitors of barium sulfate (barite), which is a common scale that poses systemic problems owing to its low solubility. We show that alginate (an acidic polysaccharide) is an anomaly among a diverse set of carboxylate-based modifiers of barite crystallization based on its ability to completely suppress both nucleation and crystal growth. Bulk crystallization assays reveal that alginate completely suppresses barite nucleation. Experiments to quantify barite crystal growth kinetics at the macroscopic level under different flow conditions revealed that alginate is also a potent inhibitor of crystal growth, with full suppression of crystallization occurring at a modifier concentration of 60 nM. Time-resolved microfluidics experiments revealed alginate's affinity to interact with all principal crystallographic faces of barite, which is uncommon among inhibitors of various inorganic crystals reported in literature. In situ atomic force microscopy experiments to probe the interactions between alginate and barite crystal surfaces revealed a transition from step bunching to step pinning modes of action at low and high alginate concentrations, respectively. The findings in this study highlight the dual roles and exceptional performance of alginate as a barite scale inhibitor. Owing to its natural abundance in brown algae, alginate is a promising and green alternative to current scale treatments.