It is still an interesting and challenging problem to synthesize a vivid and realistic singing face driven by music signal. In this paper, we present a method for this task with natural motions of the lip, facial expression, head pose, and eye states. Due to the coupling of the mixed information of human voice and background music in common signals of music audio, we design a decouple-and-fuse strategy to tackle the challenge. We first decompose the input music audio into human voice stream and background music stream. Due to the implicit and complicated correlation between the two-stream input signals and the dynamics of the facial expressions, head motions and eye states, we model their relationship with an attention scheme, where the effects of the two streams are fused seamlessly. Furthermore, to improve the expressiveness of the generated results, we propose to decompose head movements generation into speed generation and direction generation, and decompose eye states generation into the short-time eye blinking generation and the long-time eye closing generation to model them separately. We also build a novel SingingFace Dataset to support the training and evaluation of this task, and to facilitate future works on this topic. Extensive experiments and user study show that our proposed method is capable of synthesizing vivid singing face, which is better than state-of-the-art methods qualitatively and quantitatively.