Active control of terahertz wave characteristics in stretchable devices is essential for advanced terahertz applications involving large mechanical deformation or stretching. Here, a dual band terahertz active control device based on different mechanisms was designed and fabricated by combining metal metasurface with elastic film polydimethylsiloxane. Based on the deformation mismatch between metal and elastic film under tension, the double band modulation effect was realized by using the periodically sensitive cross structure metasurface. Under 36% deformation, the dipole mode and the lattice resonance mode were exploited to experimentally achieve dual-band modulation with a modulation depth of 90% and a modulation depth of 78% at 1.26 THz and 2.41 THz, respectively. The operating frequency through the lattice mode had a large dynamic range, which could be tuned from 2.41 THz to 1.85 THz. Since the mechanisms of the electric dipole resonance mode and the periodic lattice resonance mode were independent from each other, the two resonance frequencies were designed independently, which allowed the frequency interval of the dual-band modulation to be geometrically adjustable. The stretchable metasurface presented in this paper is simple to prepare, and has the advantages of large intensity modulation depth and wide frequency tuning range. It can be used not only in active control of terahertz wave, but also in passive displacement sensing.