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In this work we have suggested a solution of theGribov-Levin-Ryskin-Mueller-Qiu (GLR-MQ) nonlinear evolution equation atnext-to-next-to-leading order (NNLO). The range of $Q^2$ in which we havesolved the GLR-MQ equation is Regge region of the range $5 GeV^2 \leq Q^2 \leq25 GeV^2$ 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 thesensitivity 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 wellas for different values of Regge intercept $\lambda_G$. Our computed resultsare compared with those obtained by the most recent global DGLAP fits to theparton distribution functions viz. PDF4LHC15, NNPDF3.0, HERAPDF15, CT14 andABM12.

NNLO solution of nonlinear GLR-MQ evolution equation to determine gluon distribution function using Regge like ansatz