Actively tunable acoustic metamaterials have attracted ever increasing attention. However, their tunable frequency range is quite narrow (tens of Hz) even under ultrahigh applied voltage (about 1,000 V). Here, we report a superbroad-band actively tunable acoustic metamaterials with the bandwidth over 400 Hz under a low voltage. In the actively tunable acoustic metamaterials, the acoustic membrane is a laminated nanocomposite consisting of a poly (ethylene terephthalate) (PET) and super-aligned carbon nanotube (CNT) drawn from CNT forest array. The laminated nanocomposite membrane exhibits adjustable acoustic properties, whose modulus can be adjusted by applying external electric field. The maximum frequency bandwidth of PET/CNT nanocomposite membrane reaches 419 Hz when applying an external DC voltage of 60 V. Our actively tunable acoustic metamaterials with superbroad-band and lightweight show very promising foreground in noise reduction applications.