Large language models have enabled automated agents to tackle complex scientific research tasks, yet most existing approaches struggle to deliver scientifically rigorous and verifiable outputs. In this work, we propose a novel agent framework, TrustSciAgent, which introduces a unified evidence–reasoning–validation pipeline explicitly governed by newly formulated scientific research trustworthiness principles. TrustSciAgent structurally organizes the entire research process into pre-research, in-research, and post-research phases, ensuring that each stage strictly adheres to these principles. This design compels the agent to generate transparent, logically sound reasoning chains and deliver auditable scientific conclusions. Comprehensive experiments across four scientific domains and three representative language models demonstrate that TrustSciAgent consistently improves both the structural completeness and the correctness of reasoning outputs, outperforming standard LLM-based agents. Our results provide strong evidence that embedding domain-agnostic trustworthiness principles into the agent workflow is critical for enabling credible, generalizable, and verifiable automated scientific research.