Computer　experiments　can　emulate　the　physical　systems,　help　computational　investigations,　and　yield　analytic　solutions.　They　have　been　widely　employed　with　many　engineering　applications　(e.g.,　aerospace,　automotive,　energy　systems.　Conventional　Bayesian　optimization　did　not　incorporate　the　nested　structures　in　computer　experiments.　This　paper　proposes　a　novel　nested　Bayesian　optimization　for　complex　computer　experiments　with　multi-step　or　hierarchical　characteristics.　We　prove　the　theoretical　properties　of　nested　outputs　given　two　cases:　Gaussian　or　non-Gaussian.　The　closed　forms　of　nested　expected　improvement　are　derived.　We　also　propose　the　computational　algorithms　for　nested　Bayesian　optimization.　Three　numerical　studies　show　that　the　proposed　nested　Bayesian　optimization　outperforms　the　five　benchmark　Bayesian　optimization　methods　ignoring　the　intermediate　outputs　of　the　inner　computer　code.　The　case　study　shows　that　the　nested　Bayesian　optimization　can　efficiently　minimize　the　residual　stress　during　composite　structures　assembly　and　avoid　convergence　to　the　local　optimum.