Industrial Internet of Things (IIoT) is a new type of Internet of Things (IoT), which enables sensors to merge with several smart devices to monitor machine status, environment, and collect data from industrial devices. On the other hand, cloud computing provides a good platform for storing crowdsourced data of IIoT. Due to the semi-trusted nature of cloud computing and communication through open channels, the IIoT environment needs security services such as confidentiality and authenticity. One such solution is provided by the identity-based signcryption. Unfortunately, the identity-based signcryption approach suffers from the key escrow problem. Certificateless signcryption is the alternative of identity-based signcryption that can resolve the key escrow problem. Here, we propose a lightweight certificateless signcryption approach for crowdsourced IIoT applications with the intention of enhancing security and decreasing the computational cost and communication overhead. The security and efficiency of the proposed approach are based on the hyper elliptic curve cryptosystem. The hyper elliptic curve is the advance version of the elliptic curve having small parameters and key size of 80 bits as compared to the elliptic curve which has 160-bits key size. Further, we validate the security requirements of our approach through automated validation of Internet security protocols and applications (AVISPA) tool with the help of high level protocol specification language (HLPSL). Moreover, our lightweight and secured scheme will attract low resource devices and will become a perk in the environment of IIoT.