The green algae Scenedesmus quadricauda was immobilized in alginate gel beads. The immobilized active (IASq) and heat inactivated S. quadricauda (IHISq) were used for the removal of Remazol Brilliant Blue R (CI 61200, Reactive Blue 19, RBBR) from aqueous solutions in the concentration range 25–200 mg L − 1 . At 150 mg L − 1 initial dye concentration the IASq and IHISq exhibited the highest dye uptake capacity at 30 °C, at the initial pH value of 2.0. At the same initial dye concentration in the batch system the adsorption capacity was determined for IASq as 44.2; 44.9 and 45.7 mg g − 1 in 30, 60 and 300 min, respectively. After 300 min the adsorption capacity hardly changed during the adsorption time. The IHISq of adsorption capacity was observed as 47.6; 47.8 and 48.3 mg g − 1 in 30, 60 and 300 min, respectively. After 300 min the adsorption capacity was not changed for 24 h. The Langmuir, Freundlich, Temkin, Dubinin–Radushkevich and Flory–Huggins isotherm models were used to fit the equilibrium biosorption data. The Langmuir, Freundlich and Dubinin–Radushkevich equations have better coefficients than Temkin and Flory–Huggins equation describing the RBBR dye adsorption onto IASq and IHISq. The monomolecular biosorption capacity of the biomass was found to be 68 and 95.2 mg g − 1 for IASq and IHISq, respectively. From the Dubinin–Radushkevich model, the mean free energy was calculated as 6.42–7.15 kJ mol − 1 for IASq and IHISq, indicating that the biosorption of dye was taken place in physical adsorption reactions. The experimental data were also tested in terms of kinetic characteristics and it was determined that the biosorption process of dye was well explained with pseudo-second-order kinetics.