Large-scale vision-language models (VLMs), e.g., CLIP, learn broad visual concepts from tedious training data, showing superb generalization ability. Amount of prompt learning methods have been proposed to efficiently adapt the VLMs to downstream tasks with only a few training samples. We introduce a novel method to improve the prompt learning of vision-language models by incorporating pre-trained large language models (LLMs), called Dual-Aligned Prompt Tuning (DuAl-PT). Learnable prompts, like CoOp, implicitly model the context through end-to-end training, which are difficult to control and interpret. While explicit context descriptions generated by LLMs, like GPT-3, can be directly used for zero-shot classification, such prompts are overly relying on LLMs and still underexplored in few-shot domains. With DuAl-PT, we propose to learn more context-aware prompts, benefiting from both explicit and implicit context modeling. To achieve this, we introduce a pre-trained LLM to generate context descriptions, and we encourage the prompts to learn from the LLM's knowledge by alignment, as well as the alignment between prompts and local image features. Empirically, DuAl-PT achieves superior performance on 11 downstream datasets on few-shot recognition and base-to-new generalization. Hopefully, DuAl-PT can serve as a strong baseline. Code will be available.