Let　G　=　(V,　E)　be　a　digraph　with　nonnegative　integral　cost　and　delay　on　each　edge,　s　and　t　be　two　vertices,　and　D　∈　+0　be　a　delay　bound,　the　k　disjoint　Restricted　Shortest　Path　(kRSP)　problem　is　to　compute　k　disjoint　paths　between　s　and　t　with　the　total　cost　minimized　and　the　total　delay　bounded　by　D.　In　this　paper,　we　first　present　a　pseudopolynomial-time　algorithm　with　a　bifactor　approximation　ratio　of　(1,　2),　then　improve　the　algorithm　to　polynomial　time　with　a　bifactor　ratio　of　(1　+　∈,　2　+　∈)　for　any　fixed　∈　＞　0,　which　is　better　than　the　current　best　approximation　ratio　(O(1　+　γ),O(1　+　ln1/γ))　for　any　fixed　γ　＞　0　[3,　5].　To　the　best　of　our　knowledge,　this　is　the　first　constant-factor　algorithm　that　almost　strictly　obeys　kRSP　constraint.　Copyright　©　2015　ACM.