Sentiment analysis of user-generated reviews or comments on products and services on social media can help enterprises to analyze the feedback from customers and take corresponding actions for improvement. Training deep neural networks for textual sentiment analysis requires large-scale labeled data, which is expensive and time-consuming to obtain. Domain adaptation (DA) provides an alternate solution by learning a transferable model from another labeled source domain to the unlabeled or sparsely labeled target domain. Since the labeled data may be from multiple sources, multi- source domain adaptation (MDA) would be more practical to effectively exploit the complementary information from different domains. Existing MDA methods for textual sentiment analysis mainly focus on extracting domain-invariant features of different domains, aligning each source and the target separately, or assigning weights to the source samples statically. However, they might fail to extract some discriminative features in the target domain that are related to sentiment, neglect the correlations of different sources as well as the distribution difference among different sub- domains even in the same source, and cannot reflect the varying optimal weighting during different training stages. In this paper, we propose an instance-level multi-source domain adaptation framework, named curriculum cycle- consistent generative adversarial network (C-CycleGAN), to address the above issues. Specifically, C-CycleGAN consists of three components: (1) pre-trained text encoder which encodes textual input from different domains into a continuous representation space, (2) intermediate domain generator with curriculum instance-level adaptation which bridges the gap across source and target domains, and (3) task classifier trained on the intermediate domain for final sentiment classification. C-CycleGAN transfers source samples at an instance-level to an intermediate domain that is closer to target domain with sentiment semantics preserved and without losing discriminative features. Further, our dynamic instance- level weighting mechanisms can assign the optimal weights to different source samples in each training stage. We conduct extensive experiments on three benchmark datasets and achieve substantial gains over state-of-the-art approaches, which demonstrate the superiority of the proposed C-CycleGAN for textual sentiment classification.