Trust holds a pivotal position in contemporary society. Yet, the question of how to elevate and sustain trust among selfish individuals poses a formidable challenge. To delve into this issue, we incorporate a graded punishment strategy into a networked N-player trust game, aiming to observe the progression of trust-related behavior. Within this game framework, punishers uphold a certain degree of trust among the participants by incurring an extra expense to exclude those who betray trust. By conducting numerous Monte Carlo simulation experiments, we uncover that the graded punishment strategy can effectively curtail untrustworthy conduct to a significant degree, potentially even eliminating such behavior, thereby fostering an improvement in the overall trust level within the population. However, to effectively deploy this strategy, it is imperative to strike a balance between the penalty cost and the penalty amount, ensuring that the natural evolution of the system is not unduly disrupted. This balance is crucial for preserving the stability and sustainability of the system while safeguarding trust. Broadly speaking, our study offers fresh insights and approaches for enhancing and maintaining trust in the networked society, while also highlighting the avenues and challenges for future research, particularly in the realm of applying graded punishment strategies.