We propose a double-sided metamaterial perfect absorber (MPA) at microwave frequencies, showing absorption of 96.8% at 8.45 GHz. By employing identical front metal-patterned layer for the backside of MPA, it presents the same performance for the incident wave from both sides. Minimization of the reflectance and the transmission, by matching the impedance of free space with that of the MPA and by increasing the imaginary part of refractive index, leads to high absorption. We demonstrated the absorption mechanism with the distribution of power loss and surface current at the absorption frequencies. The polarization-insensitivity was also achieved due to the symmetric pattern, and the influence of incident angle for the TE mode was also elucidated. These properties are expected to be used in practical applications such as communication device, sensing, and imaging.