Speech-to-text translation (ST), which directly translates the source language speech to the target language text, has at- tracted intensive attention recently. However, the combina- tion of speech recognition and machine translation in a single model poses a heavy burden on the direct cross-modal cross- lingual mapping. To reduce the learning difficulty, we pro- pose COnSecutive Transcription and Translation (COSTT), an integral framework for speech-to-text translation. Our method is verified on three mainstream datasets, includ- ing Augmented LibriSpeech English-French dataset, TED English-German dataset, and TED English-Chinese dataset. Experiments show that our proposed COSTT outperforms the previous state-of-the-art methods. Our code and models will be released.