An optimization for biogas upgrading process by three-bed 12-step vacuum pressure swing adsorption (VPSA) was performed in this work. The raw gas composed of 60% CH4 and 40% CO2 was used at 313.15 K with the pressure of 101.325 kPa. Co-current replacement with heavy component step and countercurrent pressurization with replaced exhaust step were applied in the VPSA system. The results indicated that the adoption of these two steps actually helped enhance the CH4 recovery and the specific productivity of CH4. The objective pursued in this work was evaluated by the combination of the specific energy consumption, the CH4 recovery and the specific productivity of CH4. The effects of these decision variables on the objective were evaluated by the r-SQP algorithm. According to the optimization performed for a stream of biogas of 37 N m(3)/h, it was possible to obtain bio-methane with a purity of 98.00%, a recovery of 93.23% with a specific productivity of 0.1331 N m(3)/kg/h and a specific energy consumption of 0.3697 kWh/kg of produced methane. (C) 2015 Elsevier Ltd. All rights reserved.