Intelligent question answering (QA) system utilizes information retrieval and natural language processing techniques to deliver automated responses to user inquiries. Like other artificial intelligence software, intelligent QA system is prone to bugs. These bugs can degrade user experience, cause financial losses, or even trigger social panic. Therefore, it is crucial to detect and fix bugs in intelligent QA system promptly. Automated testing approaches fall into two categories. The first approach synthesizes hypothetical facts based on questions and predicted answers, then generates new questions and expected answers to detect bugs. The second approach generates semantically equivalent test inputs by injecting knowledge from existing datasets, ensuring the answer to the question remains unchanged. However, both methods have limitations in practical use. They rely heavily on the intelligent QA system’s output or training set, which results in poor testing effectiveness and generalization, especially for large-language-model-based intelligent QA systems. Moreover, these methods primarily assess semantic understanding while neglecting the logical reasoning capabilities of intelligent QA system. To address this gap, a logic-guided testing technique named QALT is proposed. It designs three logically related metamorphic relations and uses semantic similarity measurement and dependency parsing to generate high-quality test cases. The experimental results show that QALT detected a total of 9247 bugs in two different intelligent QA systems, which is 3150 and 3897 more bugs than the two current state-of-the-art techniques (i.e., QAQA and QAAskeR), respectively. Based on the statistical analysis of manually labeled results, QALT detects approximately 8073 true bugs, which is 2142 more than QAQA and 4867 more than QAAskeR. Moreover, the test inputs generated by QALT successfully reduce the MR violation rate from 22.33% to 14.37% when used for fine-tuning the intelligent QA system under test.