The phenomenal increase in the usage of Internet promotes the quality of trust in the scope of Internet of Things (IoT). Trust is beneficial in the provision of an effective, reliable, scalable, and trustworthy environment to users of the IoT network, where they can share their private information with each other on a secure communication platform. For successful communications among the Internet users, trust is an important factor to provide them with private infrastructures and secure environments, where exchanging data among devices becomes more easy and trustworthy. Therefore, trust management is a backbone for the successful and secure transmission of data among various nodes in a large-scale IoT network. To overcome the security issues, latency, and risk of malicious activities, a lightweight approach is proposed for those nodes in industrial IoT that cannot maintain security. LightTrust utilizes a centralized trust agent to generate and manage trust certificates that allow nodes to communicate for a specific time without performing trust computations. Trust agents also maintain a trust database to store the current trust degree for the aggregation/propagation purposes. Trust between two nodes is developed by direct observations in terms of compatibility, cooperativeness, and delivery ratio, whereas recommendations are used to develop trust in the context of indirect observations, i.e., experience or previous knowledge. The comparative simulations of the proposed and existing approaches are also performed whereby the results illustrate that the proposed approach efficiently maintains resilience and robust environments.