Perfect concurrent signature was introduced as an efficient approach to solving the problem of fair exchange of signatures. Almost all fair exchange e-commerce protocols 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 e-commerce protocols. This paper proposed a new concept called perfect concurrent signcryption which combined the concepts of perfect concurrent signature and signcryption together to resolve the confidentiality problem in e-commerce systems. It also proposed a certificateless perfect concurrent signcryption scheme and proved its security in the random oracle model. The scheme published the two ambiguous signcryptions in any order. Compared with the sign-then-encrypt scheme, this scheme enjoys shorter message length and less operation cost, which makes the scheme has wide application prospects.