  The effective coupling of the Higgs boson to a gluon pair is one of the most
important parameters to test the Standard Model and search for the new physics
beyond. In this paper, we propose several new observables based on the jet
energy profile to extract the effective coupling. The statistical uncertainties
of the effective coupling extracted by using new observables are derived and
estimated based on the simulation at the future $e^+e^-$ collider for $250$ GeV
center-of-mass energy and 5 ab$^{-1}$ integrated luminosity. We found that the
statistical uncertainties of effective coupling via the optimized observable
can reach about $1.6\%$ in the channels of a $Z$ boson decaying to lepton pairs
and is reduced by $52\%$ compared to the relevant uncertainties in the
conventional approach. These new observables potentially can be helpful for the
measurement of effective coupling at future $e^+e^-$ colliders.
