Speech super-resolution (SR) is a task to increase speech sampling rate bygenerating high-frequency components. Existing speech SR methods are trained inconstrained experimental settings, such as a fixed upsampling ratio. Thesestrong constraints can potentially lead to poor generalization ability inmismatched real-world cases. In this paper, we propose a neural vocoder basedspeech super-resolution method (NVSR) that can handle a variety of inputresolution and upsampling ratios. NVSR consists of a mel-bandwidth extensionmodule, a neural vocoder module, and a post-processing module. Our proposedsystem achieves state-of-the-art results on the VCTK multi-speaker benchmark.On 44.1 kHz target resolution, NVSR outperforms WSRGlow and Nu-wave by 8% and37% respectively on log spectral distance and achieves a significantly betterperceptual quality. We also demonstrate that prior knowledge in the pre-trainedvocoder is crucial for speech SR by performing mel-bandwidth extension with asimple replication-padding method. Samples can be found inhttps://haoheliu.github.io/nvsr.