As a next generation of detection technology, terahertz technology is very promising. In this work, a highly efficient terahertz wave absorber based on 3D graphene foam (3DG) is first reported. Excellent terahertz absorption property at frequency ranging from 0.1 to 1.2 THz is obtained owing to faint surface reflection and enormous internal absorption. By precise control of the constant properties for 3DG, the reflection loss (RL) value of 19 dB is acquired and the qualified frequency bandwidth (with RL value over 10 dB) covers 95% of the entire measured bandwidth at normal incidence, which far surpasses most reported materials. More importantly, the terahertz absorption performance of 3DG enhances obviously with increasing the incidence while majority of materials become invalid at oblique incidence, instead. At the incidence of 45°, the maximum RL value increases 50% from 19 to 28.6 dB and the qualified frequency bandwidth covers 100% of the measured bandwidth. After considering all core indicators involving density, qualified bandwidth, and RL values, the specific average terahertz absorption (SATA) property is investigated. The SATA value of 3DG is over 3000 times higher than those of other materials in open literatures.