  In this paper, we generalize Colding and Minicozzi's work \cite{CM} on the
stability of self-shrinkers in the hypersurface case to higher co-dimensional
cases. The first and second variation formulae of the $F$-functional are
derived and an equivalent condition to the stability in general codimension is
found. Moreover, we show that the closed Lagrangian self-shrinkers given by
Anciaux in \cite{An} are unstable.
