Background Extracellular polysaccharides (ECPs) produced by biofilm-producing marine bacterium have great applications in biotechnology, pharmaceutical, food engineering, bioremediation, and bio-hydrometallurgy industries. The ECP-producing strain was identified as Acinetobacter indicus M6 species by 16S rDNA analysis. The polymer produced by the isolate was quantified and purified and chemically analyzed, and antioxidant activities have been studied. The face-centered central composite design (FCCCD) was used to design the model. Results The results have clearly shown that the ECP was found to be endowed with significant antioxidative activities. The ECP showed 59% of hydroxyl radical scavenging activity at a concentration of 500 μg/mL, superoxide radical scavenging activity (72.4%) at a concentration of 300 μg/mL, and DPPH˙ radical scavenging activity (72.2%) at a concentration of 500 μg/mL, respectively. Further, HPLC and GC-MS results showed that the isolated ECP was a heteropolymer composed of glucose as a major monomer, and mannose and glucosamine were minor monomers. Furthermore, the production of ECP by Acinetobacter indicus M6 was increased through optimization of nutritional variables, namely, glucose, yeast extract, and MgSO4 by “Response Surface Methodology”. Moreover the production of ECP reached to 2.21 g/L after the optimization of nutritional variables. The designed model is statistically significant and is indicated by the R2 value of 0.99. The optimized medium improved the production of ECP and is two folds higher in comparison with the basal medium. Conclusions Acinetobacter indicus M6 bacterium produces a novel and unique extracellular heteropolysaccharide with highly efficient antioxidant activity. GC-MS analyses elucidated the presence of quite uncommon (1→4)-linked glucose, (1→4)-linked mannose, and (→4)-GlcN-(1→) glycosidic linkages in the backbone. The optimized medium improved the production of ECP and is two folds higher in comparison with the basal medium. The newly optimized medium could be used as a promising alternative for the overproduction of ECP.