  The complete next-to-next-to-next-to-leading order short-distance and
bound-state QCD corrections to $\Upsilon(1S)$ leptonic decay rate
$\Gamma(\Upsilon(1S)\to \ell^+\ell^-)$ has been finished by Beneke {\it et al.}
\cite{Beneke:2014qea}. Based on those improvements, we present a
renormalization group (RG) improved pQCD prediction for $\Gamma(\Upsilon(1S)\to
\ell^+\ell^-)$ by applying the principle of maximum conformality (PMC). The PMC
is based on RG-invariance and is designed to solve the pQCD renormalization
scheme and scale ambiguities. After applying the PMC, all known-type of
$\beta$-terms at all orders, which are controlled by the RG-equation, are
resummed to determine optimal renormalization scale for its strong running
coupling at each order. We then achieve a more convergent pQCD series, a
scheme- independent and more accurate pQCD prediction for $\Upsilon(1S)$
leptonic decay, i.e. $\Gamma_{\Upsilon(1S) \to e^+ e^-}|_{\rm PMC} =
1.270^{+0.137}_{-0.187}$ keV, where the uncertainty is the squared average of
the mentioned pQCD errors. This RG-improved pQCD prediction agrees with the
experimental measurement within errors.
