Travel choice analysis is crucial for understanding individual travel behavior to develop appropriate transport policies and recommendation systems in Intelligent Transportation Systems (ITS). Despite extensive research, this domain faces two critical challenges: a) modeling with limited survey data, and b) simultaneously achieving high model explainability and accuracy. In this paper, we introduce a novel prompt-learning-based Large Language Model(LLM) framework that significantly improves prediction accuracy and provides explicit explanations for individual predictions. This framework involves three main steps: transforming input variables into textual form; building of demonstrations similar to the object, and applying these to a well-trained LLM. We tested the framework's efficacy using two widely used choice datasets: London Passenger Mode Choice (LPMC) and Optima-Mode collected in Switzerland. The results indicate that the LLM significantly outperforms state-of-the-art deep learning methods and discrete choice models in predicting people's choices. Additionally, we present a case of explanation illustrating how the LLM framework generates understandable and explicit explanations at the individual level.