In　this　paper,　we　propose　a　new　nonmonotone　trust　region　Barzilai-Borwein　(BB　for　short)　method　for　solving　unconstrained　optimization　problems.　The　proposed　method　is　given　by　a　novel　combination　of　a　modified　Metropolis　criterion,　BB-stepsize　and　trust　region　method.　The　new　method　uses　the　reciprocal　of　BB-stepsize　to　approximate　the　Hessian　matrix　of　the　objective　function　in　the　trust　region　subproblems,　and　accepts　some　bad　solutions　according　to　the　modified　Metropolis　criterion　based　on　simulated　annealing　idea.　Under　some　suitable　assumptions,　the　global　convergence　of　the　new　method　is　established.　Some　preliminary　numerical　results　indicate　that,　the　new　method　is　more　efficient　compared　with　the　existing　trust　region　BB　method.