Blind signature plays an important role in cryptography. Many cryptographic researchers have made considerable achievement in this field,and have designed many schemes. However,to our knowledge,most of the existing blind signature schemes are based on the discrete logarithm problem,blinear pairings,or the RSA cryptosystem. In this paper,we propose a new blind signature scheme based on the quadratic residue. This blind signature scheme can meet the two important basic security requirements of blind signature,and because of relatively highly computational efficiency,it is suitable for mobile communications and other computationalpowerconstrained environments.