Ensuring factual consistency is crucial for natural language generation tasks, particularly in abstractive summarization, where preserving the integrity of information is paramount. Prior works on evaluating factual consistency of summarization often take the entailment-based approaches that first generate perturbed (factual inconsistent) summaries and then train a classifier on the generated data to detect the factually inconsistencies during testing time. However, previous approaches generating perturbed summaries are either of low coherence or lack error-type coverage. To address these issues, we propose AMRFact, a framework that generates perturbed summaries using Abstract Meaning Representations (AMRs). Our approach parses factually consistent 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 our approach significantly outperforms previous systems on the AggreFact-SOTA benchmark, showcasing its efficacy in evaluating factuality of abstractive summarization.