Industrial Internet of Things (IIoT) is an advanced version of IoT that actuates the sensors for monitoring and controlling the devices of industrial systems. Cloud is also one of the most popular platform used for enabling the industrial data storage and retrieval operations. But, providing security to this environment is highly demanding and essential for ensuring the privacy and confidentiality of industrial data against the malicious users. Hence, many cryptographic based security models are developed in the conventional works, which intends to securely share and retrieve data in an encrypted form by using the private and public key par. Still, it facing the major problems of high computational cost, complexity, and time consumption for processing the operations. Thus, this paper intends to develop a new IIoT-cloud framework for ensuring the security industrial data by using the certificateless signcryption mechanism. For this purpose, an Augmented Certificateless Signcryption Model (ACSM) incorporated with the Rapid Elliptic Curve Cryptosystem (RECC) is developed in this work, which objects to enhance the security of IIoT-cloud systems with reduced computational cost and time consumption. Also, it helps to avoid the key escrow problem with the ensured security properties of confidentiality, integrity, authentication, and unforgeability. For validating the performance of this mechanism, various evaluation metrics have been utilized, and also the obtained results are compared with the recent state-of-the-art models.