Target sentiment analysis aims to detect opinion targets along with recognizing their sentiment polarities from a sentence. Some models with span-based labeling have achieved promising results in this task. However, the relation between the target extraction task and the target classification task has not been well exploited. Besides, the span-based target extraction algorithm has a poor performance on target phrases due to the maximum target length setting or length penalty factor. To address these problems, we propose a novel framework of Shared-Private Representation Model (SPRM) with a coarse-to-fine extraction algorithm. For jointly learning target extraction and classification, we design a Shared-Private Network, which encodes not only shared information for both tasks but also private information for each task. To avoid missing correct target phrases, we also propose a heuristic coarse-to-fine extraction algorithm that first gets the approximate interval of the targets by matching the nearest predicted start and end indexes and then extracts the targets by adopting an extending strategy. Experimental results show that our model achieves state-of-the-art performance.