Vibrations in living environments are generally distributed over a wide frequency spectrum and exhibit multiple motion directions over time, which renders most of the current vibration energy harvesters unpractical for their harvesting purposes. Here, a 3D triboelectric nanogenerator (3D-TENG) is designed based on the coupling of the triboelectrification effect and the electrostatic induction effect. The 3D-TENG operates in a hybridization mode of conjuntioning the vertical contact-separation mode and the in-plane sliding mode. The innovative design facilitates harvesting random vibrational energy in multiple directions over a wide bandwidth. An analytical model is established to investigate the mechano-triboelectric transduction of 3D-TENG and the results agree well with experimental data. The 3D-TENG is able to harvest ambient vibrations with an extremely wide working bandwidth. Maximum power densities of 1.35 W m-2 and 1.45 W m-2 are achieved under out-of-plane and in-plane excitation, respectively. The 3D TENG is designed for harvesting ambient vibration energy, especially at low frequencies, under a range of conditions in daily life and has potential applications in environmental/infrastructure monitoring and charging portable electronics.