For　a　learning　model　to　be　effective　in　online　modeling　of　nonstationary　data,　it　must　not　only　be　equipped　with　high　adaptability　to　track　the　changing　data　dynamics　but　also　maintain　low　complexity　to　meet　online　computational　restrictions.　Based　on　these　two　important　principles,　in　this　paper,　we　propose　a　fast　adaptive　gradient　radial　basis　function　(GRBF)　network　for　nonlinear　and　nonstationary　time　series　prediction.　Specifically,　an　initial　compact　GRBF　model　is　constructed　on　the　training　data　using　the　orthogonal　least　squares　algorithm,　which　is　capable　of　modeling　variations　of　local　mean　and　trend　in　the　signal　well.　During　the　online　operation,　when　the　current　model　does　not　perform　well,　the　worst　performing　GRBF　node　is　replaced　by　a　new　node,　whose　structure　is　optimized　to　fit　the　current　data.　Owing　to　the　local　one-step　predictor　property　of　GRBF　node,　this　adaptive　node　replacement　can　be　done　very　efficiently.　Experiments　involving　two　chaotic　time　series　and　two　real-world　signals　are　used　to　demonstrate　the　superior　online　prediction　performance　of　the　proposed　fast　adaptive　GRBF　algorithm　over　a　range　of　benchmark　schemes,　in　terms　of　prediction　accuracy　and　real-time　computational　complexity.