Concurrent signature was introduced as an efficient approach to solving the problem of fair exchange of signatures. Almost all fair exchange e-commerce protocols based on concurrent signature that have been proposed until now either do not provide message privacy protection or adopt the sign-then-encrypt scheme to provide confidentiality. However, confidentiality is an important requirement of fair exchange e-commerce protocol. In this paper, a new concept called concurrent signcryption which combines the concepts of concurrent signature and signcryption together to resolve the confidentiality problem in e-commerce systems based on concurrent signature. We also propose a concurrent signcryption scheme using bilinear pairings and prove its security in the random oracle model. Compared with the sign-then-encrypt scheme using bilinear pairings, our scheme enjoys shorter message length and less operation cost. Moreover, in our scheme the two ambiguous signcryptions can be published in any order.