  In the paper, we study the $\Upsilon(1S)$ leptonic decay width
$\Gamma(\Upsilon(1S)\to \ell^+\ell^-)$ by using the principle of maximum
conformality (PMC) scale-setting approach. The PMC adopts the renormalization
group equation to set the correct momentum flow of the process, whose value is
independent to the choice of the renormalization scale and its prediction thus
avoids the conventional renormalization scale ambiguities. Using the known
next-to-next-to-next-to-leading order perturbative series together with the PMC
single scale-setting approach, we do obtain a renormalization scale independent
decay width, $\Gamma_{\Upsilon(1S) \to e^+ e^-} = 1.262^{+0.195}_{-0.175}$ keV,
where the error is squared average of those from
$\alpha_s(M_{Z})=0.1181\pm0.0011$, $m_b=4.93\pm0.03$ GeV and the choices of
factorization scales within $\pm 10\%$ of their central values. To compare with
the result under conventional scale-setting approach, this decay width agrees
with the experimental value within errors, indicating the importance of a
proper scale-setting approach.
