In　this　letter,　we　conduct　a　comprehensive　investigation　on　tail-biting　(TB)　spatially　coupled　protograph　(SC-P)　low-density　parity-check　(LDPC)　codes　under　shuffled　belief-propagation　(BP)　decoding.　We　first　propose　a　shuffled　extrinsic　information　transfer　(S-EXIT)　algorithm　tailored　for　the　shuffled　decoding.　Exploiting　the　proposed　algorithm,　we　accurately　predict　the　convergence　performance　(i.e.,　decoding　thresholds)　for　TB-SC-P　codes　under　such　a　schedule　and　demonstrate　that　their　convergence　performance　can　be　further　improved.　Based　on　the　S-EXIT　analysis,　we　develop　an　optimization　method　to　generate　a　new　type　of　TB-SC-P　codes,　called　improved　TB-SC　double-protograph　(I-TB-SC-DP)　codes,　which　can　inherit　the　superiorities　of　two　mother　protograph　codes　and　possess　more　desirable　decoding　thresholds.　Theoretical　analyses　and　simulated　results　illustrate　that　the　proposed　I-TB-SC-DP　codes　exhibit　better　error　performance　than　the　existing　counterparts.