In　this　paper,　we　propose　a　simulated　annealing-based　Barzilai-Borwein　(SABB)　gradient　method　for　unconstrained　optimization　problems.　The　SABB　method　accepts　the　Barzilai-Borwein　(BB)　step　by　a　simulated　annealing　rule.　If　the　BB　step　cannot　be　accepted,　the　Armijo　line　search　is　used.　The　global　convergence　of　the　SABB　method　is　established　under　some　mild　conditions.　Numerical　experiments　indicate　that,　compared　to　some　existing　BB　methods　using　nonmonotone　line　search　technique,　the　SABB　method　performs　well　with　high　efficiency.