Noise pollution has been recognized as one of the leading environmental problems worldwide and has a negative impact on the physiological and psychological health of humans. Various porous polymeric materials have been found to be inefficient for sound absorption, especially in low-frequency interval; in addition, these materials have other disadvantages such as hygroscopicity and flammability. Herein, an efficient and economical semi-open cellular structure consisting of tiny self-assembled graphene oxide (GO) sheets interrupted by functionalized carbon nanotubes (CNT) was demonstrated as an acoustic composite foam. This innovative composite foam exhibits an approximately 100% and 20% enhancement over a band gap between 250 and 1600 Hz as compared to the pure melamine foam and graphene oxide-incorporated melamine foam with a thickness of 20 mm, respectively. The semi-open cellular structure results in optimal air-flow resistance, tortuosity against sound wave propagation, smaller viscous characteristic lengths, internal reflection and interfacial damping; hence, the composite foam shows advanced energy exhaustion and improved acoustic absorption. Furthermore, the inclusion of GO and CNT provides other properties including moisture insulation and fire retardancy. This kind of innovative sound absorbing material is inexpensive, easy to synthesize and environmentally friendly for commercial and industrial applications.