  The explanation for lepton $g-2$ anomalies is provided with the nonlocal QED
which is the simple extension of the standard model. This solution is based on
the same gauge symmetry as QED without introducing any new particles and
interactions. The correlation functions in the nonlocal strength tension and
lepton-photon interaction make it possible to explain the discrepancies of both
$\Delta a_\mu$ and $\Delta a_e$. With the same approach, the discrepancy of
anomalous magnetic moment of $\tau$ lepton from standard model is estimated in
the range $1.19\times10^{-5}$ to $3.21\times10^{-3}$ which is covered by the
current experimental uncertainty.
