End-to-end speech translation aims to translate speech in one language into text in another language via an end-to-end way. Most existing methods employ an encoder-decoder structure with a single encoder to learn acoustic representation and semantic information simultaneously, which ignores the speech-and-text modality differences and makes the encoder overloaded, leading to great difficulty in learning such a model. To address these issues, we propose a Speech-to-Text Adaptation for Speech Translation (STAST) model which aims to improve the end-to-end model performance by bridging the modality gap between speech and text. Specifically, we decouple the speech translation encoder into three parts and introduce a shrink mechanism to match the length of speech representation with that of the corresponding text transcription. To obtain better semantic representation, we completely integrate a text-based translation model into the STAST so that two tasks can be trained in the same latent space. Furthermore, we introduce a cross-modal adaptation method to close the distance between speech and text representation. Experimental results on English-French and English-German speech translation corpora have shown that our model significantly outperforms strong baselines, and achieves the new state-of-the-art performance.