One　of　the　major　obstacles　in　using　radial　basis　function　(RBF)　neural　networks　is　the　convergence　toward　local　minima　instead　of　the　global　minima.　For　this　reason,　an　adaptive　gradient　multiobjective　particle　swarm　optimization　(AGMOPSO)　algorithm　is　designed　to　optimize　both　the　structure　and　parameters　of　RBF　neural　networks　in　this　paper.　First,　the　AGMOPSO　algorithm,　based　on　a　multiobjective　gradient　method　and　a　self-adaptive　flight　parameters　mechanism,　is　developed　to　improve　the　computation　performance.　Second,　the　AGMOPSO-based　self-organizing　RBF　neural　network　(AGMOPSO-SORBF)　can　optimize　the　parameters　(centers,　widths,　and　weights),　as　well　as　determine　the　network　size.　The　goal　of　AGMOPSO-SORBF　is　to　find　a　tradeoff　between　the　accuracy　and　the　complexity　of　RBF　neural　networks.　Third,　the　convergence　analysis　of　AGMOPSO-SORBF　is　detailed　to　ensure　the　prerequisite　of　any　successful　applications.　Finally,　the　merits　of　our　proposed　approach　are　verified　on　multiple　numerical　examples.　The　results　indicate　that　the　proposed　AGMOPSO-SORBF　achieves　much　better　generalization　capability　and　compact　network　structure　than　some　other　existing　methods.