Inspired by the recent near-threshold J/ψ photoproduction measurements, we discuss gluon gravitational form factors (GFFs) and internal properties of the proton. This work presents a complete set analysis of the proton gluon GFFs connecting the gluon part of the energy-momentum tensor and the heavy quarkonium pho toproduction. In particular, the gluon GFFs as functions of the squared momentum transfer t are determined by a global fitting of the J/ψ differential and total cross section experimental data. Combined with the quark contributions to the D-term form factor extracted from the deeply virtual Compton scattering experiment, the total D-term are obtained to investigate their applications for the description of the proton mechanical properties. These researches provide a unique perspective for studying the proton gluon GFFs and important information for improving QCD constraints on the gluon GFFs. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.