Purpose　-　The　purpose　of　this　paper　is　to　attempt　to　realize　a　distribution　network　optimization　in　supply　chain　using　grey　systems　theory　for　uncertain　information.　Design/methodology/approach　-　There　is　much　uncertain　information　in　the　distribution　network　optimization　of　supply　chain,　including　fuzzy　information,　stochastic　information　and　grey　information,　etc.　Fuzzy　information　and　stochastic　information　have　been　studied　in　supply　chain,　however　grey　information　of　the　supply　chain　has　not　been　covered.　In　the　distribution　problem　of　supply　chain,　grey　demands　are　taken　into　account.　Then,　a　mathematics　model　with　grey　demands　has　been　constructed,　and　it　can　be　transformed　into　a　grey　chance-constrained　programming　model,　grey　simulation　and　a　proposed　hybrid　particle　swarm　optimization　are　combined　to　resolve　it.　An　example　is　also　computed　in　the　last　part　of　the　paper.　Findings　-　The　results　are　convincing:　not　only　that　grey　system　theory　can　be　used　to　deal　with　grey　uncertain　information　about　distribution　of　supply　chain,　but　grey　chance-constrained　programming,　grey　simulation　and　particle　swarm　optimization　can　be　combined　to　resolve　the　grey　model.　Practical　implications　-　The　method　exposed　in　the　paper　can　be　used　to　deal　with　distribution　problems　with　grey　information　in　the　supply　chain,　and　network　optimization　results　with　a　grey　uncertain　factor　could　be　helpful　for　supply　chain　efficiency　and　practicability.　Originality/value　-　The　paper　succeeds　in　realising　both　a　constructed　model　of　the　distribution　of　supply　chain　with　grey　demands　and　a　solution　algorithm　of　the　grey　mathematics　model　by　using　one　of　the　newest　developed　theories:　grey　systems　theory.