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Talking head synthesis is an emerging technology with wide applications in film dubbing, virtual avatars and online education. Recent NeRF-based methods generate more natural talking videos, as they better capture the 3D structural information of faces. However, a specific model needs to be trained for each identity with a large dataset. In this paper, we propose Dynamic Facial Radiance Fields (DFRF) for few-shot talking head synthesis, which can rapidly generalize to an unseen identity with few training data. Different from the existing NeRF-based methods which directly encode the 3D geometry and appearance of a specific person into the network, our DFRF conditions face radiance field on 2D appearance images to learn the face prior. Thus the facial radiance field can be flexibly adjusted to the new identity with few reference images. Additionally, for better modeling of the facial deformations, we propose a differentiable face warping module conditioned on audio signals to deform all reference images to the query space. Extensive experiments show that with only tens of seconds of training clip available, our proposed DFRF can synthesize natural and high-quality audio-driven talking head videos for novel identities with only 40k iterations. We highly recommend readers view our supplementary video for intuitive comparisons. Code is available in https://sstzal.github.io/DFRF/.