Space-based Internet of things (S-IoT) can provide global services and connection capabilities. It has broad emerging application, including marine monitoring, forest monitoring, animal monitoring, disaster emergency response and other fields. However, owing to the openness of satellite communications, S-IoT is vulnerable to hijacking attacks, and malicious attackers can tamper with or forge transmitted messages. More seriously, due to limited S-IoT node resources, it is difficult to directly apply existing security solutions to terrestrial networks to the S-IoT. In this study, we propose CSP, a novel, secure, and efficient scheme based on certificateless signatures and bilinear pairings for S-IoT. CSP consists of six phases: system setup, partial private key settings, private key settings, public key settings, signing and verifying. In CSP, we especially design that part of the private key comes from the ground KGC and the other part is generated by the communication entity itself. We theoretically prove CSP is secure, and it is able to resist tampering or forgery attacks. Moreover, it can also ensure the authenticity, integrity, unforgeability, and nonrepudiation of transmitted messages. We also conducted extensive experiments and compared CSP with the existing schemes. The experimental results demonstrate that CSP can significantly reduce the total scheme time consumption. Especially, it can reduce about 50–60% of the time in the signature verification phase.