We present our study of the differential cross section for the Higgs boson production in $k_T$-factorization framework. The $k_T$-factorization formalism includes a convolution over unintegrated parton distribution functions (uPDF) and off-shell parton level matrix element. The off-shell matrix element calculated considering initial gluons to be off-shell. We have considered only gluon fusion process which is dominant production mechanism for the Higgs boson production at LHC. We have used Ciafaloni-Catani-Fiorani-Marchesini (CCFM) uPDF based on CCFM evolution equations. We have compared our results with fixed order estimates up to NNLO+NNLL obtained using HRes tool within collinear factorization framework as well as with the ATLAS and CMS measurements of the corresponding differential distributions. This study will play an important role in understanding differential cross section within $k_T$-factorization framework.