The dual Meissner effect is described and numerically observed in a gauge-invariant way in lattice Monte-Carlo simulations of pure SU(2) QCD. A gauge-invariant monopole-like quantity on the lattice is defined by a gauge-invariant Abelian-like field strength. The Abelian-like field strength is expressed in terms of a unit-vector in color space which is constructed by a non-Abelian field strength itself. It is just equal to the absolute value of the corresponding non-Abelian field strength except for the sign. In this note we show the theoretical background and most numerical results will be published in a separate report  in this conference.