In　this　article,　an　adaptive　prescribed-time　neural　controller　is　developed　for　the　tracking　problem　of　a　class　of　high-order　nonlinear　systems　with　full-state　constraints.　First,　a　prescribed-time　bounded　stability　criterion　is　designed.　Then,　to　handle　the　＂explosion　of　complexity＂　problem　of　the　backstepping　method,　an　adaptive　prescribed-time　filter　is　constructed,　in　which　the　filter　error　is　prescribed-time　stable.　Compared　with　existing　methods,　the　newly　designed　transformation　approach　can　accommodate　a　broader　range　of　state　constraint　types.　Then,　the　unknown　nonlinear　function　is　handled　by　radial　basis　function　neural　networks　(RBFNNs).　The　adaptive　prescribed-time　neural　control　scheme　is　developed　based　on　above.　It　can　guarantee　that　the　closed-loop　system　achieves　the　prescribed-time　stability,　and　all　states　do　not　transgress　the　constraints.　To　demonstrate　the　effectiveness　of　the　control　strategy,　comparative　simulations　are　provided　at　the　end.