Despite remarkable achievements, automatic speech recognition (ASR) in low-resource scenarios still faces two challenges: high-quality data scarcity and high computational demands. This paper proposes EThai-ASR, the first to apply large language models (LLMs) to Thai ASR and create an efficient LLM-based ASR system. EThai-ASR comprises a speech encoder, a connection module and a Thai LLM decoder. To address the data scarcity and obtain a powerful speech encoder, EThai-ASR introduces a self-evolving data refinement strategy to refine weak labels, yielding an enhanced speech encoder. Moreover, we propose a pluggable sequence compression module used in the connection module with three modes designed to reduce the sequence length, thus decreasing computational demands while maintaining decent performance. Extensive experiments demonstrate that EThai-ASR has achieved state-of-the-art accuracy in multiple datasets. We release our refined text transcripts to promote further research.