As　to　the　problem　of　time　series　prediction　for　small　sample　data　with　time　delays,　the　dynamic　changes　of　system　time　delays　should　be　considered　and　expressed　in　the　process　of　modeling.　This　paper　extends　the　GM(1,1|τi)　model　to　a　more　applicable　GM(1,1|τi)　model,　which　contains　a　time-varying　delay　function　to　describe　the　possible　time-varying　delays　in　series.　An　efficient　algorithm　for　the　model　parameter　estimation　is　given,　together　with　the　time　response　formula　of　GM(1,1|τi)　model.　Parameters　of　the　time-varying　delay　function　used　in　the　model　algorithm　are　optimized　by　the　gray　correlation　degree　theory.　The　method　designed　in　this　paper　improves　the　fitting　degree　of　the　GM(1,1|τi)　model　to　the　analyzed　sequence.　It　also　helps　to　analyze　the　development　trend　of　system　based　on　the　mathematical　properties　of　time-varying　delay　functions.　Finally,　the　model　is　applied　to　forecast　the　cargo　throughput　of　coastal　ports　in　Fujian　province,　and　the　results　are　compared　with　those　based　on　GM(1,1)　and　GM(1,1,τ).　Results　show　that　the　GM(1,1|τi)　model　has　higher　modeling　precision　when　the　raw　data　contains　complex　time-varying　delays　and　this　will　enlarge　the　class　of　existing　grey　series　prediction　models　with　time　delays.　©　2019,　Editorial　Board　of　Journal　of　Systems　Engineering　Society　of　China.　All　right　reserved.