Due to the rapid development of computing hardware resources and the dramatic growth of data, pre-trained models in speech recognition, such as Whisper, have significantly improved the performance of speech recognition tasks. However, these models usually have a high computational overhead, making it difficult to execute effectively on resource-constrained devices. To speed up inference and reduce model size while maintaining performance, we propose a novel guided knowledge distillation and quantization for large pre-trained model Whisper. The student model selects distillation and quantization layers based on quantization loss and distillation loss, respectively. We compressed $\text{Whisper}_\text{small}$ to $\text{Whisper}_\text{base}$ and $\text{Whisper}_\text{tiny}$ levels, making $\text{Whisper}_\text{small}$ 5.18x/10.48x smaller, respectively. Moreover, compared to the original $\text{Whisper}_\text{base}$ and $\text{Whisper}_\text{tiny}$, there is also a relative character error rate~(CER) reduction of 11.3% and 14.0% for the new compressed model respectively.