Neural　ordinary　differential　equations　(Neural　ODE)　interprets　deep　networks　as　discretization　of　dynamical　systems,　and　has　shown　great　promise　in　the　physical　science,　modeling　irregular　time　series,　and　mean　field　games.　The　Neural　ODE　comsumes　a　long　time　training　process,　which　is　arguably　one　of　the　main　stumbling　blocks　towards　their　widespread　adoption.　To　improve　the　convergence　speed　of　training,　in　this　parper,　we　formulate　the　training　task　as　a　separable　nonlinear　optimization　problem,　and　propose　a　separable　training　algorithm　based　on　a　nonmonotone　trust-region　method.　The　proposed　algorithm　uses　the　variable　projection　strategy　to　reduce　the　dimension　of　variables　by　solving　a　subproblem　and　then　the　trust-region　method　is　used　to　optimize　the　reduced　function.　To　accelerate　the　convergence　speed,　we　introduce　the　nonmonotone　strategy　to　make　the　update　of　trust-region　radius　elastic　and　employ　the　adaptive　technology　that　uses　the　gradient　information　of　the　objective　function　to　update　the　radius.　Numerical　results　confirm　the　effectiveness　of　the　proposed　algorithm.