This　paper　focuses　on　the　tracking-control　problem　of　nonlinear　strict-feedback　system　by　utilizing　neural　networks.　Combining　a　novel　recurrent　neural　network　and　gradient-based　neural　network,　we　investigate,　develop　and　design　a　new　controller　based　on　the　synthesized　neural　network　model　(N-G　model)　to　track　the　output　trajectory　performance　of　the　nonlinear　strict-feedback　system.　This　presented　control　scheme　could　have　a　good　output　tracking　performance　for　the　nonlinear　strict-feedback　system.　For　comparing　with　the　presented　N-G　model,　the　classic　backstepping　design　method　is　also　employed　to　design　the　control　input　for　the　nonlinear　strict-feedback　control　system　in　this　paper.　The　computer　simulation　results　demonstrate　that　the　controller　based　on　the　N-G　model　could　be　used　to　tackle　the　tracking-control　problem　with　accuracy　and　effectiveness,　together　with　the　faster　convergent　speed　than　that　based　on　the　backstepping　algorithm.　Generally　speaking,　with　the　appropriate　increase　of　design　parameters,　the　controller　based　on　the　N-G　model　could　improve　convergence　performance　for　nonlinear　strict-feedback　system.