Low frequency sound attenuation is a challenging task, because of the severe mass, stiffness and volume constraints on the absorbing and/or reflecting barriers. Recently, significant improvements in low frequency sound attenuation has been achieved by introducing the acoustic metafoam concept, which combines the mechanism of conventional acoustic foams - high viscothermal dissipation - with the working principle of locally resonant acoustic metamaterials - wave attenuation at low frequencies. However, the attenuation improvement provided by periodic materials containing identical resonators is confined to a narrow frequency range. To overcome this limitation, graded acoustic metafoams are proposed and studied here, where a distribution of local resonators with varying properties (mass and stiffness) is introduced. It is demonstrated that, through a suitable design of mass and stiffness distribution of the resonators, the broadening of the frequency attenuation ranges can be effectively achieved. Graded acoustic metafoams are, therefore, a natural development direction for achieving broad frequency attenuation zones.