Taking into account both the intrinsic curvature and Zeeman effects, persistent currents in a multi-walled carbon nanotorus are explored by using a supercell method, within the tight-binding formalism. It is shown that in the absence of the Zeeman effect, the intrinsic curvature induces some dramatic changes in energy spectra and thus changes in the shape of the flux-dependent current. A paramagnetism-diamagnetism transition is observed. With consideration of the Zeeman splitting energy, the period of persistent current is destroyed, and a diamagnetism-paramagnetism transition is obtained at high magnetic field. In addition, we further explore the effect of external electric field energy (Eef) on persistent current, indicating that it changes unmonotonously with Eef. Taking into account both the intrinsic curvature and Zeeman effects, persistent currents in a multi-walled carbon nanotorus are explored by using a supercell method, within the tight-binding formalism. It is shown that in the absence of Zeeman effect, the intrinsic curvature inductive some dramatic changes in energy spectra and thus changes in the shape of the flux-dependent current. A paramagnetism-diamagnetism transition is observed. With consideration of the Zeeman splitting energy, the period of persistent current is destroyed, and a diamagnetism-paramagnetism transition is obtained at high magnetic field. addition, we further explore the effect of external electric field energy (Eef) on persistent current, indicating that it changes unmonotonously with Eef.