This paper proposes a source-filter-based generative adversarial neural vocoder named SF-GAN, which achieves high-fidelity waveform generation from input acoustic features by introducing F0-based source excitation signals to a neural filter framework. The SF-GAN vocoder is composed of a source module and a resolution-wise conditional filter module and is trained based on generative adversarial strategies. The source module produces an excitation signal from the F0 information, then the resolution-wise convolutional filter module combines the excitation signal with processed acoustic features at various temporal resolutions and finally reconstructs the raw waveform. The experimental results show that our proposed SF-GAN vocoder outperforms the state-of-the-art HiFi-GAN and Fre-GAN in both analysis-synthesis (AS) and text-to-speech (TTS) tasks, and the synthesized speech quality of SF-GAN is comparable to the ground-truth audio.