Nowadays,　Electronic　Medical　Records　(EHRs)　are　closely　linked　to　people＇s　social　lives.　In　order　to　ensure　the　convenience　of　medical　services,　many　related　organizations　need　to　share　EHRs　across　organizations　to　exchange　information.　The　existing　private　EHR　shareable　schemes　still　contain　some　security　issues,　e.g.,　unreliability　of　cloud　service　provider,　complex　key　calculation　and　unreliable　backward　security.　In　this　paper,　we　propose　an　attribute-based　access　control　scheme　based　on　the　smart　contract　(ABAC-SC).　By　virtue　of　the　blockchain　technique,　ABAC-SC　can　be　directly　embedded　into　the　existing　private　EHRs　shareable　system　to　solve　existing　unsafe　problems.　Considering　the　storage　constraints　of　the　blockchain,　a　data　processing　solution　is　designed　to　reduce　the　storage　requirements　of　the　pre-data　upload　process.　We　simulate　our　ABAC-SC　scheme　in　Ethereum＇s　test　network　Rinkeby,　and　the　experimental　results　show　the　feasibility　of　our　solution.　©　2019　IEEE.