Automatic action quality assessment (AQA) has attracted more interests due to its wide applications. However, existing AQA methods usually employ the multi-branch models to generate multiple scores, which is not flexible for dealing with a variable number of judges. In this paper, we propose a novel Uncertainty-Driven AQA (UD-AQA) model to generate multiple predictions only using one single branch. Specifically, we design a CVAE (Conditional Variational Auto-Encoder) based module to encode the uncertainty, where multiple scores can be produced by sampling from the learned latent space multiple times. Moreover, we output the estimation of uncertainty and utilize the predicted uncertainty to re-weight AQA regression loss, which can reduce the contributions of uncertain samples for training. We further design an uncertainty-guided training strategy to dynamically adjust the learning order of the samples from low uncertainty to high uncertainty. The experiments show that our proposed method achieves new state-of-the-art results on the Olympic events MTL-AQA and surgical skill JIGSAWS datasets.