Along with the technology evolution for dense integration of high-power, high-frequency devices in electronics, the accompanying interfacial heat transfer problem leads to urgent demands for advanced thermal interface materials (TIMs) with both high through-plane thermal conductivity and good compressibility. Most metals have satisfactory thermal conductivity but relatively high compressive modulus, and soft silicones are typically thermal insulators (0.3 W m–1 K–1). Currently, it is a great challenge to develop a soft material with the thermal conductivity up to metal level for TIM application. This study solves this problem by constructing a graphene-based microstructure composed of mainly vertical graphene and a thin cap of horizontal graphene layers on both the top and bottom sides through a mechanical machining process to manipulate the stacked architecture of conventional graphene paper. The resultant graphene monolith has an ultrahigh through-plane thermal conductivity of 143 W m–1 K–1, exceeding that of many metals, and a low compressive modulus of 0.87 MPa, comparable to that of silicones. In the actual TIM performance measurement, the system cooling efficiency with our graphene monolith as TIM is 3 times as high as that of the state-of-the-art commercial TIM, demonstrating the superior ability to solve the interfacial heat transfer issues in electronic systems.