End-to-end interpretation is currently the prevailing paradigm for remote sensing fine-grained ship classification (RS-FGSC) task. However, its inference process is uninterpretable, leading to criticism as a black box model. To address this issue, we propose a large vision-language model (LVLM) named IFShip for interpretable fine-grained ship classification. Unlike traditional methods, IFShip excels in interpretability by accurately conveying the reasoning process of FGSC in natural language. Specifically, we first design a domain knowledge-enhanced Chain-of-Thought (COT) prompt generation mechanism. This mechanism is used to semi-automatically construct a task-specific instruction-following dataset named TITANIC-FGS, which emulates human-like logical decision-making. We then train the IFShip model using task instructions tuned with the TITANIC-FGS dataset. Building on IFShip, we develop an FGSC visual chatbot that redefines the FGSC problem as a step-by-step reasoning task and conveys the reasoning process in natural language. Experimental results reveal that the proposed method surpasses state-of-the-art FGSC algorithms in both classification interpretability and accuracy. Moreover, compared to LVLMs like LLaVA and MiniGPT-4, our approach demonstrates superior expertise in the FGSC task. It provides an accurate chain of reasoning when fine-grained ship types are recognizable to the human eye and offers interpretable explanations when they are not.