Abstract: Verifiably encrypted signature is useful in handling the fair exchange problem, especially online contract signing. A new ID-based verifiably encrypted signature scheme is proposed based on Shim signature scheme. The new scheme does not use any zero-knowledge proofs to provide verifiability, thus eliminates some computation burden from complicated interaction. The creation of verifiably encrypted signature in the scheme is realized by adding a value into one parameter of Shim signature. The verification of verifiably encrypted signature in the scheme is implemented by multiplying one pairing value with the right part of verification equation in Shim signature. Taking account of above reasons, the design of the proposed scheme is compact. The new scheme is provably secure in the random oracle model under the CDH problem assumption. The analysis results show that the presented scheme needs smaller communication requirements and its computation complexity is more optimized compared with the previous ID-based verifiably encrypted signature schemes. ID-based public key cryptography has become a good alternative for certificate based public key setting, especially when efficient key management and moderate security are required. Our new verifiably encrypted signature scheme is an entirely ID-based scheme, which provides an efficient primitive for building fair exchange protocols in ID-based public key cryptosystem.