  We introduce a U(1) lattice gauge theory with dual gauge fields and study its
phase structure. This system is motivated by unconventional superconductors
like extended s-wave and d-wave superconductors in the strongly-correlated
electron systems. In this theory, the "Cooper-pair" field is put on links of a
cubic lattice due to strong on-site repulsion between electrons in contrast to
the ordinary s-wave Cooper-pair field on sites. This Cooper-pair field behaves
as a gauge field dual to the electromagnetic U(1) gauge field. By Monte Carlo
simulations we study this lattice gauge model and find a first-order phase
transition from the normal state to the Higgs (superconducting) state. Each
gauge field works as a Higgs field for the other gauge field. This mechanism
requires no scalar fields in contrast to the ordinary Higgs mechanism.
