  We studied the dimension-6 leptonic anomalous gauge couplings in the
formulation of linearly realized gauge symmetry effective Lagrangian and
investigated the constraints on these anomalous couplings from the existed
experimental data including LEP2 and $W$/$Z$ boson decay. Some bounds of
$O(0.1-10){\rm TeV}^{-2}$ on four relevant anomalous couplings are given by the
Z factories. We studied the sensitivity of testing the leptonic anomalous
couplings via the process $e^+e^-\rightarrow W^+W^-$ at future $e^+e^-$ linear
colliders. We discussed different sensitivities to anomalous couplings at
polarized and unpolarized $e^+e^-$ colliders, respectively, with 500 GeV and 1
TeV collision energy. Our results show that the a 500 GeV ILC can provide a
test of the anomalous couplings, with the same relative uncertainty of cross
section measurement, of $O(0.1-1){\rm TeV}^{-2}$, and a 1 TeV ILC can test the
anomalous couplings of $O(0.01-0.1){\rm TeV}^{-2}$.
