We present a recurrent encoder-decoder deep neural network architecture that directly translates speech in one language into text in another. The model does not explicitly transcribe the speech into text in the source language, nor does it require supervision from the ground truth source language transcription during training. We apply a slightly modified sequence-to-sequence with attention architecture that has previously been used for speech recognition and show that it can be repurposed for this more complex task, illustrating the power of attention-based models. A single model trained end-to-end obtains state-of-the-art performance on the Fisher Callhome Spanish-English speech translation task, outperforming a cascade of independently trained sequence-to-sequence speech recognition and machine translation models by 1.8 BLEU points on the Fisher test set. In addition, we find that making use of the training data in both languages by multi-task training sequence-to-sequence speech translation and recognition models with a shared encoder network can improve performance by a further 1.4 BLEU points.