  We calculated a differential cross section of the Higgs boson production in
the $h\to ZZ^*\to 4\ell$ decay channel within the framework of
$k_T$-factorization. Results are obtained using an off-shell matrix element for
the $g^*g^*\to h\to ZZ^*\to 4\ell$ process together with
Ciafaloni-Catani-Fiorani-Marchesini (CCFM) evolution equations for an
unintegrated gluon distribution function. We have presented a comparison of our
results with the latest experimental measurements at $\sqrt{S}$ = 8 TeV and
$\sqrt{S}$ = 13 TeV from the ATLAS and CMS collaborations at the LHC. In
addition to this, we have compared our results with the results from the
collinear factorization formalism calculated up to next-to-next-to-leading
order plus next-to-next-to-leading logarithm (NNLO + NNLL) accuracy obtained
using the HRes code for the Higgs boson production in the gluon-gluon fusion
process. Our estimates are consistently close to NNLO + NNLL results obtained
using a collinear factorization formalism and are also in agreement with
experimental measurements.
