Bayesian　inference　methods　usually　require　numerous　forward　model　simulations　to　generate　converged　samples.　When　the　forward　model　is　expensive　to　evaluate,　it　becomes　a　challenging　problem　to　estimate　the　posterior　distribution　function　from　Bayesian　inference.　We　propose　a　computationally　efficient　Bayesian　inference　method　with　a　combination　of　polynomial　chaos　and　Gibbs　sampling　for　structural　damage　detection　and　condition　assessment.　The　likelihood　function　is　approximated　with　the　polynomial　chaos　expansion,　and　the　Gibbs　sampling　method　is　performed　to　generate　the　samples　for　the　posterior　distribution.　In　the　Gibbs　sampling,　the　forward　model　is　not　required,　which　reduces　the　computation　time　for　Bayesian　inference.　The　proposed　Bayesian　inference　method　is　conducted　to　update　the　probability　distributions　of　unknown　structural　parameters　for　structural　condition　assessment,　and　the　observer　data　comprise　the　correlation　function　of　the　acceleration　responses.　The　analytical　formula　for　the　correlation　function　of　the　acceleration　response　is　also　derived　in　this　study.　Both　numerical　studies　and　experimental　studies　were　conducted　to　verify　the　accuracy　and　efficiency　of　the　proposed　method.　The　results　show　that　the　posterior　distribution　of　unknown　parameters　can　be　successfully　estimated　by　using　the　proposed　method.　In　addition,　the　proposed　improved　Bayesian　inference　is　robust　to　measurement　noise.　Comparison　studies　with　the　original　Gibbs　sampling　method　are　presented.　The　results　indicate　that　the　proposed　improved　Bayesian　inference　method　is　about　100　times　faster　than　the　original　Gibbs　sampling　method.　©　2022　John　Wiley　&　Sons,　Ltd.