Existing server-aided attribute-based signature (SA-ABS) to secure industrial Internet of Things (IIoT)-oriented applications raise challenges such as achieving collusion attack resilience and realizing expressive linear secret-sharing scheme (LSSS) access structures. In this paper, we positively address these challenges by proposing a novel SA-ABS for IIoT. Distinct from the existing works in this field, our SA-ABS protocol not only allows to delegate the heavy calculation in both signature generation and verification to a third-party server, but also resists the collusion attack and realizes expressive LSSS access structures. The formal proof about the unforgeability of the proposed SA-ABS has been given on the basis of the standard model. Theoretical analysis as well as experimental simulation reveal the fact that the proposed SA-ABS is feasible and efficient.