The parton distribution functions (PDFs) of the proton are one of the essential ingredients to describe physics processes at hadron colliders. The Z boson production data at the LHC have a potential to constrain PDFs, especially the gluon distribution. In this study the CMS measurement of the inclusive double differential Z boson production cross section in terms of transverse momentum and rapidity is compared to the next-to-leading order theory predictions at the center-of-mass energy, s=8 TeV with an integrated luminosity of 19.71 fb-1. In addition, the sensitivity of this measurement to PDFs is studied within the framework of the HERAFitter. A moderate improvement to the gluon distribution is observed at the Bjorken x≈0.1 region. However, in order to obtain further improvement to the gluon distribution in the global fits, the higher-order theory calculations accessible via fast techniques are necessary.