A topological current is shown to exist in superconductivity. Using th
e phi-mapping topological current theory, we have obtained a rigorous
London equation with topological current, which reveals the inner rela
tion between the condensate wave function psi and the induction (B) ov
er right arrow. It is also shown that the equation is characterized by
the Hopf index and Brouwer degree of phi mapping. As a result, the so
-called modified London equation, which describes the distribution of
the magnetic field for isolated vortices, is only a special case of th
e equation. Our theory, obtained without using any particular models o
r hypotheses, can also be applied to the illustration of a vortex-anti
vortex pair, vortex ring, and multicharged vortex. [S0163-1829(98)0402
5-9].