Ensuring factual consistency is crucial in various natural language processing tasks, particularly in abstractive summarization, where preserving the integrity of information is paramount. Prior entailment-based approaches often generate factually inconsistent summaries and then train a classifier on the generated data. However, summaries produced by these approaches are either of low coherence or lack error-type coverage. To address these issues, we propose AMRFact, a novel framework that generates factually inconsistent summaries using Abstract Meaning Representation (AMR). Our approach parses factually correct summaries into AMR graphs and injects controlled factual inconsistencies to create negative examples, allowing for coherent factually inconsistent summaries to be generated with high error-type coverage. Additionally, we present a data selection module NegFilter based on natural language inference and BARTScore to ensure the quality of the generated negative samples. Experimental results demonstrate that our approach significantly outperforms previous systems on the AggreFact-SOTA dataset, showcasing its efficacy in assessing factuality in abstractive summarization.