Speech-to-text translation (ST), which directly translates the source language speech to the target language text, has attracted intensive attention recently. However, the combination 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 propose COnSecutive Transcription and Translation (COSTT), an integral approach for speech-to-text translation. The key idea is to generate source transcript and target translation text with a single decoder. It benefits the model training so that additional large parallel text corpus can be fully exploited to enhance the speech translation training. Our method is verified on three mainstream datasets, including 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. The code is available at https://github.com/dqqcasia/st.