  The momentum space subtraction (MOM) scheme is one of the most frequently
used renormalization schemes in perturbative QCD (pQCD) theory. In the paper,
we make a detailed discussion on the gauge dependence of the pQCD prediction
under the MOM scheme. Conventionally, there is renormalization scale ambiguity
for the fixed-order pQCD predictions, which assigns an arbitrary range and an
arbitrary error for the fixed-order pQCD prediction. The principle of maximum
conformality (PMC) adopts the renormalization group equation to determine the
magnitude of the coupling constant and hence determines an effective momentum
flow of the process, which is independent to the choice of renormalization
scale. There is thus no renormalization scale ambiguity in PMC predictions. To
concentrate our attention on the MOM gauge dependence, we first apply the PMC
to deal with the pQCD series. We adopt the Higgs boson decay width,
$\Gamma(H\to gg)$, up to five-loop QCD contributions as an example to show how
the gauge dependence behaves before and after applying the PMC. It is found
that the Higgs decay width $\Gamma (H\to gg)$ depends very weakly on the
choices of the MOM schemes, being consistent with the renormalization group
invariance. It is found that the gauge dependence of $\Gamma(H\to gg)$ under
the $\rm{MOMgg}$ scheme is less than $\pm1\%$, which is the smallest gauge
dependence among all the mentioned MOM schemes.
