Graphene is a typical two-dimensional (2D) allotrope form of carbon. Excellent optical and electric properties of graphene, such as broadband absorption and high mobility of carriers, promise prosperous applications in optic and optoelectronic devices. However, flat graphene structures (either graphene film on a structural substrate or structural graphene) hardly support efficient excitation of high-order plasmonic modes, which results in a serious deficiency in realizing efficient light-matter interaction in graphene-based devices. Here, by configuring the flat graphene into complex three-dimensional (3D) pillars, strong high-order plasmonic modes were observed and verified numerically and experimentally. It is found that, despite the influence of geometry and material parameters on resonance, the excitation efficiency of high-order modes is highly dependent on the graphene on the sidewall of pillars. Therefore, the proposed 3D graphene structures not only retain the merits of 2D materials but also introduce a new dimension to control the light-matter interaction. In addition, the fabrication technique in this work can be readily applied to other 2D materials with various geometric shapes. It is believed that the proposed 3D form of 2D materials will ignite a plethora of unprecedented designs and applications in THz communication such as THz pulse generators, modulators, detectors, and spectrometers.