Background Increasing environmental awareness is forcing waste creators to consider new options such as biosorption for the disposal of colored wastewaters. Due to prohibitive costs of commercially available activated carbon, low-cost biosorbents with high adsorption capacities have gained increasing attention. The present investigation deals with utilization of a low-cost, fungal biosorbent of Rhizopus arrhizus NCIM 997 and optimization of conditions for the removal of Reactive Orange 13 dye from an aqueous solution using sequential statistically designed experiments.Results Plackett-Burman design with six independent variables (pH, temperature, biosorbent dosage, dye concentration, contact time and speed of agitation) was used to identify the most important factors influencing dye biosorption. Path of steepest ascent and central composite design were used to move toward the vicinity of the optimum operating conditions and to determine the optimum levels of the variables, respectively. The maximum biosorption capacity (133.63 mg/g) was obtained under the following conditions: pH 2.0, dye concentration 114 mg/L, biosorbent dosage 0.8 g/L and speed of agitation 85 rpm. Validation experiments and application of artificial neural network showed excellent correlation between predicted and experimental values. Conclusions Response surface methodology using central composite design was employed at the specified combinations of four independent significant factors identified by Plackett-Burman design. The fitted model was used to arrive at the best operating conditions to achieve a maximum response. Sequential optimization was successfully used to increase biosorption by 49.04 %. The study indicated that the fungal biosorbent was an effective and economical alternative for the removal of Reactive Orange 13 dye.