Nowadays, acoustic and electromagnetic pollution problems are becoming increasingly serious. Thus, electromagnetic interference (EMI) shielding materials and high acoustic insulation materials are urgently needed. EMI shielding materials and high acoustic insulation materials or structures have been rapidly developed. However, electromagnetic yet acoustic shielding (double-shielding) structures have not been reported so far. Herein, we propose a novel metastructure based on a graphene paper and artificial honeycomb, which exhibits not only excellent electromagnetic interference shielding property but also robust acoustic shielding efficiency. The EMI shielding effectiveness of the metastructure is up to 74 dB in a broad range from 2.6 to 26.5 GHz. The acoustic shielding effectiveness reaches 25 dB from 200 to 1500 Hz. It is worth noting that the effectiveness of acoustic shielding reaches up to 40 dB at very low frequency of 200 Hz. A typical double-shielding application demo was assembled to prove the attenuation performance against electromagnetic waves and sound. Our unique metastructure is very promising for protecting from electromagnetic and acoustic pollution.