Real-life　civil　structures　often　stay　in　a　grey　situation　due　to　lack　of　knowledge　and　measurements.　In　a　poor　information　condition,　classic　Bayesian　inference　is　practically　difficult　to　perform　owing　to　intractable　likelihood　functions.　Under　such　circumstance,　a　structure　should　be　defined　as　a　grey　system.　Thereby,　a　grey　Bayesian　inference　framework　has　been　proposed　by　incorporating　the　grey　theory　with　approximate　Bayesian　computation　for　damage　assessment　purposes.　Structural　parameters　are　represented　by　interval　grey　variables,　whose　grey　kernels　and　degrees　of　greyness　are　used　to　define　probability　distributions　for　sampling.　A　grey　population　Monte　Carlo　sampler　has　also　been　developed　by　introducing　interval　grey　numbers　and　an　evolutionary　particle　pool　into　the　particle　filtering　process.　A　novel　particle　interchange　mechanism　is　simultaneously　proposed　for　effective　particle　interflow.　Meanwhile,　stochastic　response　surfaces　are　used　to　correlate　structural　parameters　with　responses　for　fast　response　computation.　Also,　likelihood　calculation　is　replaced　with　a　distance　measure　between　simulated　and　measured　samples.　Lastly,　the　proposed　inference　strategy　has　been　verified　against　both　the　numerical　and　experimental　beams　having　the　different　damage　scenarios.　The　damage　locations　and　severities　were　successfully　identified　by　the　changes　in　the　grey　intervals　and　kernels.　©　2021　John　Wiley　&　Sons,　Ltd.