The existing identity-based bidirectional proxy re-signature schemes require expensive bilinear pairing operations. Focused on the issue, an identity-based bidirectional proxy re-signature scheme without bilinear pairing was presented by using hash function. Under the assumption of discrete logarithm difficult problem, the proposed proxy re-signature scheme was proved secure against forgery under adaptive chosen message attacks. Furthermore, the proposed scheme was bidirectional, versatile, transparent and key optimal,which eliminated the bilinear pairing operations. Compared with the identity-based bidirectional proxy re-signature scheme — Shao scheme, the proposed scheme could reduce the computational complexity of re-signature algorithm and improve the computation efficiency of signature verification algorithm. Based on the proposed scheme, an aggregate proxy re-signature scheme was proposed. The new scheme can aggregate re-signatures only if they are generated in the same time period, which can greatly reduce the communication overhead.