  We present a precise theoretical prediction for the signal-background
interference process of $gg(\to h^*) \to ZZ$, which is useful to constrain the
Higgs boson decay width and to measure Higgs couplings to the SM particles. The
approximate NNLO $K$-factor is in the range of $2.05-2.45$ ($1.85-2.25$),
depending on $M_{ZZ}$, at the 8 (13) TeV LHC. And the soft gluon resummation
can increase the approximate NNLO result by about $10\%$ at both the 8 TeV and
13 TeV LHC. The theoretical uncertainties including the scale, uncalculated
multi-loop amplitudes of the background and PDF$+\alpha_s$ are roughly
$\mathcal{O}(10\%)$ at ${\rm NNLL'}$. We also confirm that the approximate
$K$-factors in the interference and the pure signal processes are the same.
