Based on the tight-binding model of π electrons for a graphite sheet, the electronic structure of the chiral toroidal carbon nanotubes(TCNTs) has been derived.The quantum properties and magnetic pattern of TCNTs have been investigated in detail in this paper. A magnetic field can induce a metal-semiconductor transition for typeⅠ and Ⅱ TCNTs.The computation and analysis also show: when- T=0K, the magnetism of typeⅠand Ⅱ TCNTs are a linearly function of the magnetic flux Φ, with a period Φ0(h/e),which is sensitive to chiral angle θ,toroidal width r and temperture T, independent of toroidal radius R. The magnetism of chiral TCNTs is much stronger than that of the armchair or zigzag TCNTs. The magnetism of type Ⅲ TCNTs is very weak,without regularity.