  In this work we have suggested a solution of the
Gribov-Levin-Ryskin-Mueller-Qiu (GLR-MQ) nonlinear evolution equation at
next-to-next-to-leading order (NNLO). The range of $Q^2$ in which we have
solved the GLR-MQ equation is Regge region of the range $5 GeV^2 \leq Q^2 \leq
25 GeV^2$ and so we have incorporated the Regge like behavior to obtain $Q^2$
evolution of gluon distribution function $G(x, Q^2)$. We have also checked the
sensitivity of our results for different values of correlation radius (R)
between two interacting gluons, viz. $R=2 GeV^{-1}$ and $R= 5 GeV^{-1}$ as well
as for different values of Regge intercept $\lambda_G$. Our computed results
are compared with those obtained by the most recent global DGLAP fits to the
parton distribution functions viz. PDF4LHC15, NNPDF3.0, HERAPDF15, CT14 and
ABM12.
