Radial　basis　function　neural　network　(RBFNN)　is　one　of　the　most　popular　neural　networks,　and　an　appropriate　selection　of　its　structure　and　learning　algorithms　is　crucial　for　its　performance.　Aiming　to　alleviate　the　sensitivity　of　the　RBFNN　to　its　parameters　and　improve　the　overall　performance　of　the　network,　this　study　proposes　a　Gaussian　Membership-based　online　self-organizing　RBF　neural　network　(GM-OSRBFNN).　First,　the　Gaussian　Membership　is　introduced　to　enhance　network　insensitivity　to　network　parameters　and　used　as　a　similarity　metric　to　indicate　the　similarity　between　the　sample　to　a　hidden　neuron　and　that　between　hidden　neurons.　Second,　the　similarity　metric　is　used　to　design　the　neuron　addition　and　merging　rules　to　achieve　a　self-organizing　network　structure,　and　error　constraints　are　introduced　to　the　neuron　addition　rule;　also,　the　noisy　neuron　deletion　rule　is　defined　to　make　the　network　structure　more　compact.　In　addition,　an　online　fixed　mini-batch　gradient　algorithm　is　used　for　online　learning　of　network　parameters,　which　can　guarantee　fast　and　stable　convergence　of　the　network.　Finally,　the　proposed　GM-OSRBFNN　is　tested　on　common　nonlinear　system　modeling　problems　to　verify　its　effectiveness.　The　experimental　results　show　that　compared　to　the　existing　models,　the　GM-OSRBFNN　can　achieve　competitive　prediction　performance　with　a　more　compact　network　structure,　faster　convergence　speed,　and,　more　importantly,　better　insensitivity　to　network　parameters.　©　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature　2025.