Aiming at the shortcomings of the current electronic cash scheme in anonymity and fairness, two schemes based on elliptic curve and bilinear pair were proposed. The schemes can not only guarantee the anonymity of customers, but also trace the double-spending to ensure the fairness of the transaction. Firstly, the electronic cash scheme based on elliptic curve authentication encryption proposed by Chaudhry et al. was analyzed, which can not guarantee the anonymity of consumption and effectively resolve the transaction disputes. Then the scheme of bank delegating offline electronic cash scheme proposed by Liu et al. was also analyzed, and it was found that the users in it can fake electronic money. Two improved schemes were proposed to modify the above defects and the security of them were analyzed. The analysis show that the new schemes not only inherit the security and efficiency of the previous schemes, and can resist replay attacks and impersonation attacks, but also ensure the anonymity and fairness of the schemes.