Recently, the Industrial Internet of Things (IIoT) has become increasingly important for applications in the industry. IIoT has essentially become a prime security focus for implementing secure communication. Among the available cryptographic tools, identity-based signcryption provide a sound solution to fulfill the security requirement of IIoT. On the other hand a generalized proxy signcryption can work adaptively as proxy signature and proxy signcryption using a single algorithm. In order to accomplish effective and on-time communication whenever the manager of the company went out for a usual business trip or an IIoT device which has lack of resources, then it must need to delegate her/his signcryption rights to their subordinates (proxy agents/device). For this purpose, to make the delegation procedure more efficient and reliable, we proposed a lightweight identity-based generalized proxy signcryption (IBGPS) scheme for IIoT. The IBGPS scheme is provably secure in terms of indistinguishability against adaptive chosen ciphertext attack (IND − IBGPS − CCA) and existential unforgeable against a possible adaptive chosen message attack (EUF − IBGPS − CMA) under Hyperelliptic Curve Decisional Diffie-Hellman problem (HEDHP) and Hyperelliptic Curve Discrete Logarithm problem (HECDLP) in the random oracle model. Furthermore the performance evaluation in terms of computation and communication costs shows that the IBGPS scheme is more effective than the existing schemes.