Diffusion model-based vocoders have exhibited outstanding performance in the realm of speech synthesis. However, owing to the curved nature of generation path, they necessitate traversing numerous steps to guarantee the speech quality, hindering their applicability in real-world scenarios. In this paper, we propose SWave (Code and speech samples are available at https://swave-demo.github.io/ ), a novel vocoder based on rectified flow which improves the efficiency of speech synthesis by Straightening the Waveform generation path. Specifically, we employ rectification to transform the noise distribution into the data distribution with a probability flow that is as straight as possible. Subsequently, we use distillation and fine-tuning to further enhance the generation efficiency and quality, respectively. Experiments on the LJSpeech dataset demonstrate that compared with other vocoders such as FastDiff and WaveGrad, SWave enhances the generation efficiency. In particular, with a straightforward sampling schedule, SWave generates comparable speech to WaveGrad with significantly fewer steps (2 steps vs 25 steps).