A smart grid is a new ecosystem, which is made by combining a number of smart Internet of Things (IoT) devices that manage wide energy sources by increasing the efficiency and reliability of the smart energy systems. As the IoT devices in the smart grid ecosystem generate a gigantic amount of data that needs to be stored and managed in the cloud server. On the other hand, the stored data in the cloud server can be accessible to a number of data users, therefore the data need authenticity and secrecy. Here, to fulfill the security requirements of such type of communication, signcryption with proxy re-encryption technique is the most suitable option where a semi-trusted third party can alter a ciphertext that has been encrypted for one user into another ciphertext without seeing the original content of the message. However, the existing signcryption with proxy re-encryption schemes for the smart grid environment is suffering from more bandwidth space and greater computational time requirements. Thus, in this paper, we propose a lightweight certificate-based signcryption with a proxy re-encryption (CBSRE) scheme for smart grid based-IoT devices with the intention of reducing the computational and communicational costs. For the security and efficiency of the proposed CBSRE scheme, we used a hyperelliptic curve cryptosystem that uses small parameters with a key size of 80-bits. Furthermore, the proposed scheme provides the security requirements of confidentiality (IND-CBSRE-CCA2-I and IND-CBSRE-CCA2-II), unforgeability (EUF-CBSRE-CMA-I and EUF-CBSRE-CMA-II) and forward secrecy. Additionally, we compared our proposed CBSRE scheme with the existing proxy signcryption with re-encryption schemes and the final results show that the new scheme provides strong security with the expanse of minimal computational and communications resources.