Graphene is an ideal material for high-performance photodetectors because of its superior electronic and optical properties. However, graphene’s weak optical absorption limits the photoresponsivity of conventional photodetectors based on planar (two-dimensional or 2D) back-gated graphene field-effect transistors (GFETs). Here, we report a self-rolled-up method to turn 2D buried-gate GFETs into three-dimensional (3D) tubular GFETs. Because the optical field inside the tubular resonant microcavity is enhanced and the light-graphene interaction area is increased, the photoresponsivity of the resulting 3D GFETs is significantly improved. The 3D GFET photodetectors demonstrated room-temperature photodetection at ultraviolet, visible, mid-infrared and terahertz (THz) regions, with both ultraviolet and visible photoresponsivities of more than 1 A/W, and photoresponsivity of 0.232 A/W at 3.11 THz. The electrical bandwidth of these devices exceeds 1 MHz. This combination of high photoresponsivity, a broad spectral range and high speed will lead to new opportunities for 3D graphene optoelectronic devices and systems.