In this paper we have solved the nonlinear Gribov–Levin–Ryskin–Mueller–Qiu (GLR-MQ) evolution equation for the gluon distribution function $$G(x,Q^2)$$ G ( x , Q 2 ) and studied the effects of the nonlinear GLR-MQ corrections to the Leading Order (LO) Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) evolution equations. Here we have incorporated a Regge-like behavior of gluon distribution function to obtain the solution of the GLR-MQ evolution equation. We have also investigated the $$Q^2$$ Q 2 -dependence of the gluon distribution function from the solution of the GLR-MQ evolution equation. Moreover it is interesting to observe from our results that nonlinearities increase with decreasing correlation radius ( $$R$$ R ) between two interacting gluons. The results also confirm that the steep behavior of gluon distribution function is observed at $$R=5\,\mathrm{GeV}^{-1}$$ R = 5 GeV - 1 , whereas it is lowered at $$R=2\,\mathrm{GeV}^{-1}$$ R = 2 GeV - 1 with decreasing $$x$$ x as $$Q^2$$ Q 2 increases. In this work we have also checked the sensitivity of $$\lambda _\mathrm{G}$$ λ G in our calculations. Our computed results are compared with those obtained by the global DGLAP fits to the parton distribution functions viz. GRV, MRST, MSTW and with the EHKQS model.