To address the common issue of cloud server authority abuse in Proxy Re-Encryption （PRE） schemes， as well as limitations of the existing Conditional Proxy Re-Encryption （CPRE） schemes in terms of multiple receivers， security， and computational cost， a Certificate-Based Conditional Broadcast Proxy Re-Encryption （CB-CBPRE） scheme was proposed. In the scheme， an access condition was set by the data owner when generating convertible ciphertext and re-encryption key， and a valid re-encrypted ciphertext only generated by the cloud server when the condition matched， thereby preventing the cloud server from abusing its authority and providing re-encrypted ciphertext to unauthorized users. The security of the proposed scheme was a Decisional Diffie-Hellman （DDH） problem， and ciphertext of the proposed scheme was proven to be indistinguishable in Random Oracle Model （ROM）. Experimental results show that when the number of receivers is 50， compared with four schemes： Identity-Based Broadcast Proxy Re-Encryption （IB-BPRE）， Privacy-Preserving Proxy Re-Encryption （PP-PRE）， Revocable Identity-Based Broadcast Proxy Re-Encryption （RIB-BPRE）， and Multi-Channel Broadcast Proxy Re-Encryption （MC-BPRE）， the proposed scheme reduces the computational time by 73%， 83%， 87%， and 92%， respectively， and the communication volume by 66%， 90%， 77%， and 66%， respectively， enhancing efficiency of encryption effectively.