A medical adhesive comprises a hydrophilic urethane prepolymer (UP) obtained by reacting a fluorine-containing nonaromatic polyisocyanate component (A) and a polyol component (B) having a hydrophilic polyol (B1), and a phenolic radical scavenger (PRS). The content of (PRS) is preferably 0.01 to 3% by weight based on the weight of (UP). The content of oxyethylene groups in (B) is preferably 30 to 100% by weight based on the weight of the oxyalkylene groups in (B). Preferably, (B) is a mixture of a random copolymer obtained by addition of ethylene oxide and propylene oxide to diols and polypropylene glycol. The content of isocyanate groups in the medical adhesive is 1 to 10% by weight based on the weight of (UP). The medical adhesive is suitable for bonding body tissues, such as lung, artery and heart in particular.