Visual question answering (VQA) is a task where an image is given, and a series of questions are asked about the image. To build an efficient VQA algorithm, a large amount of QA data is required which is very expensive. Generating synthetic QA pairs based on templates is a practical way to obtain data. However, VQA models trained on those data do not perform well on complex, human-written questions. To address this issue, we propose a new method called chain of QA for human-written questions (CoQAH). CoQAH utilizes a sequence of QA interactions between a large language model and a VQA model trained on synthetic data to reason and derive logical answers for human-written questions. We tested the effectiveness of CoQAH on two types of human-written VQA datasets for 3D-rendered and chest X-ray images and found that it achieved state-of-the-art accuracy in both types of data. Notably, CoQAH outperformed general vision-language models, VQA models, and medical foundation models with no finetuning. The source code for CoQAH is available [10].