Compression and purification unit (CPU) is a common industrial process for capturing CO2 from oxy-fuel combustion where high energy requirement is one of its disadvantages. This study focuses on analyzing of the sensitivity and optimizing multi-objectively the operating conditions of CPU, using response surface methodology (RSM). The main objective was to increase the efficiency of CO2 removal from the oxy-fuel combustion power plant. Statistical analysis reveals that reducing the first separator temperature, not only, plays a major role in CO2 separation, but also, it decreases the total work and heat duty of the process. It was found that the optimal multi-stage CO2 compressor discharge pressure was 2534 bar while regular pressure for this process was reported as 30 bar Furthermore, the optimal flue gas temperature before, between and after compression, and the first and second flash separator temperatures were 20 degrees C, 20 degrees C, 20.6 degrees C, -38.2 degrees C, and -55 degrees C, respectively. with the previous works carried out in a constant amount of CO2 separation, the proposed process leads to lower pressure, and therefore lower operating and capital costs. (C) 2017 Elsevier Ltd. All rights reserved.