A series of batch lab-scale experiments were performed to investigate the performance of dead phosphorylated algal biomass of Spirogyra species for the bioadsorption of Cu$^{+2}$ ions from aqueous solutions. FT-IR and SEM analyses were performed to characterize the phosphorylated and raw algae. The SEM analysis indicated that the phosphorus content increases by about 5 times. The isotherm equilibrium data indicated that phosphorylation enhances the removal of Cu$^{+2}$ from water by about 20%. The experimental isotherms fit well to Langmuir models with $R^{2}$ values close to 0.99. Adsorption kinetic study was conducted to investigate the effect of initial Cu$^{+2}$ concentrations, pH, and adsorbent dose on the loading capacity of algal biomass. The optimum pH for the process was around 6 and the corresponding maximum loading capacity was 65 mg/g. The pseudo second-order kinetics successfully modeled the kinetic results with $R^{2}$ values closed to 0.99. The thermodynamic results indicated that the bioadsorption process is endothermic and spontaneous at initial Cu$^{+2}$ concentrations lower than 100 mg/L. The results were promising and encourage the design of a continuous process using algal biomass to remediate water polluted with heavy metals.