Fast inference speed is an important goal towards real-world deployment of speech translation (ST) systems. End-to-end (E2E) models based on the encoder-decoder architecture are more suitable for this goal than traditional cascaded systems, but their effectiveness regarding decoding speed has not been explored so far. Inspired by recent progress in non-autoregressive (NAR) methods in text-based translation, which generates target tokens in parallel by eliminating conditional dependencies, we study the problem of NAR decoding for E2E-ST. We propose a novel NAR E2E-ST framework, Orthros, in which both NAR and autoregressive (AR) decoders are jointly trained on the shared speech encoder. The latter is used for selecting better translation among various length candidates generated from the former, which dramatically improves the effectiveness of a large length beam with negligible overhead. We further investigate effective length prediction methods from speech inputs and the impact of vocabulary sizes. Experiments on four benchmarks show the effectiveness of the proposed method in improving inference speed while maintaining competitive translation quality compared to state-of-the-art AR E2E-ST systems.