For the problem that secure and efficient cross-domain authentication (between Public Key Infrastructure (PKI) and Certificateless Public Key Cryptography (CLC)) in different cryptosystems cannot be achieved in cryptosystems that already existed and frequently interacted, a signcryption based heterogeneous cross-domain identity authentication method was proposed in cloud environment. The cross-domain identity authentication was re-established for heterogeneous systems, two different cryptosystems (PKI↔CLC) between Users (U) and Cloud Service Provider (CSP) was designed, the calculation of cross-domain authentication of domain management center was removed, and the third party inter-cloud authentication center (CA) was introduced to complete mutual information authentication between U and CSP, the signcryption algorithm was adopted to complete the signcryption for the U in different security domains, as a result, the bidirectional entity cross-domain identity authentication of heterogeneous system was realized and the computing overhead of U was reduced. Compared with anonymous authentication and proxy re-signature, the efficiency of the proposed cross-domain authentication is improved by 53.5% and 23.2% respectively. In addition, the method realizes legality, authenticity and security of U identities in different cryptosystems and has the ability to resist replay attack, replacement attack and man-in-the-middle attack.