We　propose　a　new　biometric　identity　based　encryption　scheme　(Bio-IBE),　in　which　user　biometric　information　is　used　to　generate　the　public　key　with　a　fuzzy　extractor.　This　is　the　first　Bio-IBE　scheme　that　achieves　constant　size　ciphertext.　This　is　also　a　scheme　that　is　secure　against　the　adaptive　chosen　ciphertext　attack　(CCA2).　Details　are　presented　along　with　a　discussion　of　Shamir＇s　threshold　secret　sharing　and　fuzzy　extraction　of　biometrics,　which　is　based　on　error　correction　codes.　We　also　define　a　security　model　and　prove　that　the　security　of　the　proposed　scheme　is　reduced　to　the　decisional　bilinear　Diffie-Hellman　(DBDH)　assumption.　The　comparison　shows　that　the　proposed　scheme　has　better　efficiency　and　stronger　security　compared　with　the　available　Bio-IBE　schemes.