In　this　paper,　searching　for　a　better　chloride　ions　sub-diffusion　system,　a　multi-term　time-fractional　derivative　diffusion　model　is　proposed　for　the　description　of　the　time-dependent　chloride　ions　penetration　in　reinforced　concrete　structures　exposed　to　chloride　environments.　We　prove　the　stability　and　convergence　of　the　model.　We　use　the　modified　grid　approximation　method　(MGAM)　to　estimate　the　fractional　orders　and　chloride　ions　diffusion　coefficients　in　the　reinforced　concrete　for　the　multi-term　time　fractional　diffusion　system.　And　then　to　verify　the　efficiency　and　accuracy　of　the　proposed　methods　in　dealing　with　the　fractional　inverse　problem,　two　numerical　examples　with　real　data　are　investigated.　Meanwhile,　we　use　two　methods　of　fixed　chloride　ions　diffusion　coefficient　and　variable　diffusion　coefficient　with　diffusion　depth　to　simulate　chloride　ions　sub-diffusion　system.　The　result　shows　that　with　the　new　fractional　orders　and　parameters,　our　multi-term　fractional　order　chloride　ions　sub-diffusion　system　is　capable　of　providing　numerical　results　that　agree　better　with　the　real　data　than　other　models.　On　the　other　hand,　it　is　also　noticed　from　the　numerical　solution　of　the　chloride　ions　sub-diffusion　system　that　setting　the　variable　diffusion　coefficient　with　diffusion　depth　is　more　reasonable.　And　it　is　also　found　that　chloride　ions　diffusion　coefficients　in　reinforced　concrete　should　be　decreased　with　diffusion　depth　which　is　completely　consistent　with　the　theory.　In　addition,　the　model　can　be　used　to　predict　the　chloride　profiles　with　a　time-dependent　property.　This　article　is　part　of　the　theme　issue　＇Advanced　materials　modelling　via　fractional　calculus:　challenges　and　perspectives＇.　©　2020　The　Author(s).