The space information network (SIN) has attracted more and more attention due to its extensive applicability and great expanding access services. The complicated properties of SIN, such as the dynamic and unstable topology, the highly exposed links and so on, make it necessary to design an appropriate key management scheme to ensure the security of communication. In this paper we propose an anonymous and distributed certificate-less key management scheme (aCL-KMS) for SIN. It mainly adopts the strategy of the distributed key generation, update and agreement instead of the complex centralized key management. Based on the certificate-less public key cryptosystem (CL-PKC), this scheme not only avoids the high cost of complicated certificate management, but also overcome the key-escrow problem of the certificate-based or identity-based public key cryptosystem. Also, due to the fact that the anonymous authentication mechanism adopts the temporary identification of members, this scheme can efficiently protect the members' privacy and ensure the confidentiality of communications. The security properties discussion and the computational overhead analysis show that the proposed key management system is secure enough to meet the security requirements of SIN, and it is of less computing cost at the same time.