We present the design, numerical simulations and experimental measurements of an asymmetric cross terahertz metamaterial absorber (MPA) on ultra-flexible polyimide film. The perfect metamaterial absorber composed of two structured metallic layers separated with a polyimide film with a total thickness of functional layers much smaller than the operational wavelength. Two distinct absorption peaks are found at resonance frequencies of 0.439THz and 0.759 THz with resonance amplitude of near unity, which are in good agreement with the simulation results. The sample is also measured by a THz-TDS imaging system to illustrate the absorption characterization. The scanning images show that the sample could act as a perfect absorber at specific resonance frequencies while a perfect reflector at off resonance frequencies. To illustrate the physical mechanism behind these spectral responses, the distribution of the power loss and surface current are also presented. The result shows that the incident wave is trapped and absorbed by the polyimide dielectric layer at different vicinities of the proposed asymmetric cross MPA for the two absorption peaks. Furthermore, the index sensing performance of the structure is also investigated, and the calculated sensitivity is 90GHz/RIU for f1 mode and 154.7GHz/RIU for f2 mode, indicating that the higher frequency resonance absorption peak has better potential applications in sensing and detection. The ultra-flexible, low cost, high intensity dual band terahertz absorbers may pave the way for designing various terahertz functional devices, such as ultrasensitive terahertz sensors, spatial light modulators and filters.