In the present study, biosorption behavior of a green filamentous alga, spirogyra in its native and modified states was investigated for copper removal from an electroplating industrial effluent. For this, the effluent containing 194 mg·L−1 Cu2+ in sulfate medium was contacted with both forms of spirogyra, under the parametric variations of effluent pH, adsorbent dosage, contact time, and sorption temperature. The study revealed spirogyra as a prominent candidate for removing contaminant metal cation; however, at the same condition, biosorption capacity of modified biomass in gel form was higher than the native spirogyra. At the optimized condition with 6 g sorbent dosage treated to 100 mL effluent for 30 min at pH 6.0 and temperature 20 °C, the maximum 82.8% and 96.4% copper could be adsorbed by the native and modified spirogyra, respectively. The batch sorption data using native biomass followed pseudo-first-order kinetic; exhibiting the multilayer sorption mechanism via surface diffusion could be defined by the Freundlich model. In contrast, the sulfuric acid treated modified spirogyra followed pseudo-second-order kinetics and intra particle diffusion as the rate-limiting step.