It　is　well-known　that　tensor　eigenvalues　have　been　widely　used　in　signal　processing,　diffusion　tensor　imaging,　independent　component　analysis　and　other　fields.　Effective　methods　for　solving　Z-eigenvalues　of　large-scale　tensors　tend　to　fall　into　a　local　optimal　region.　The　feasible　trust-region　method　is　an　effective　method　for　computing　the　extreme　Z-eigenvalue　of　large-scale　tensors,　but　it　also　tends　to　fall　into　the　local　optimal.　To　overcome　the　problem,　we　propose　three　global　optimization　strategies　based　on　the　feasible　trust-region　method　to　improve　the　success　rate　of　computing　the　extreme　Z-eigenvalue.　The　first　one　is　a　multi-initial　points　algorithm.　The　second　one　is　a　simulated　annealing　algorithm.　The　third　one　is　an　infeasible　trust-region　algorithm　which　constructs　an　infeasible　trust-region　subproblem,　expanding　the　search　scope　and　expecting　to　improve　the　success　rate.　We　prove　the　global　convergence　of　the　infeasible　trust-region　algorithm.　The　numerical　results　show　that　the　success　rate　of　calculating　the　extreme　Zeigenvalue　is　greatly　increased　with　the　help　of　the　global　optimization　strategy.