Interval　type-2　fuzzy　neural　network　(IT2FNN)　is　widely　used　to　model　nonlinear　systems.　Unfortunately,　the　gradient　descent-based　IT2FNN　with　uncertain　variances　always　suffers　from　low　convergence　speed　due　to　its　inherent　singularity.　To　cope　with　this　problem,　a　nonsingular　gradient　descent　algorithm　(NSGDA)　is　developed　to　update　IT2FNN　in　this　article.　First,　the　widths　of　type-2　fuzzy　rules　are　transformed　into　root　inverse　variances　(RIVs)　that　always　satisfy　the　sufficient　condition　of　differentiability.　Second,　the　singular　RIVs　are　reformulated　by　the　nonsingular　Shapley-based　matrices　associated　with　type-2　fuzzy　rules.　It　averts　the　convergence　stagnation　caused　by　zero　derivatives　of　singular　RIVs,　thereby　sustaining　the　gradient　convergence.　Third,　an　integrated-form　update　strategy　(IUS)　is　designed　to　obtain　the　derivatives　of　parameters,　including　RIVs,　centers,　weight　coefficients,　deviations,　and　proportionality　coefficient　of　IT2FNN.　These　parameters　are　packed　into　multiple　subvariable　matrices,　which　are　capable　to　accelerate　gradient　convergence　using　parallel　calculation　instead　of　sequence　iteration.　Finally,　the　experiments　showcase　that　the　proposed　NSGDA-based　IT2FNN　can　improve　the　convergence　speed　through　the　improved　learning　algorithm.