We design and demonstrate a flexible, ultrathin and double-sided metamaterial perfect absorber (MPA) at 2.39 terahertz (THz), which enables excellent light absorbance under incidences from two opposite sides. Herein, the MPA is fabricated on a λ0/10.1-thick flexible polyethylene terephthalate substrate of εr = 2.75 × (1 + 0.12i), sandwiched by two identical randomized metallic patterns by our stochastic design process. Such an MPA provides tailored permittivity and permeability to approach the impedance of free space for minimizing reflectance and a great imaginary part of the refractive index for reducing transmittance and finally results in high absorbance. Both experimental measurement and numerical simulation are in a good agreement. The flexible, ultrathin and double-sided MPA significantly differs from traditional quarter-wavelength absorbers and other single-sided perfect absorbers, paving a way toward practical THz applications in thermal emission, sensing and imaging, communications, stealth technique, and even energy harvesting.