The recent years have witnessed the widespread of light field imaging in interactive and immersive visual applications. To record the directional information of the light rays, larger storage space is required by light field images compared with conventional 2D images. Hence, the efficient compression of light field image is highly desired for further applications. In this paper, we propose a novel light field image compression scheme using multi- branch spatial transformer networks based view synthesis. Firstly, a sparse subset of views are selected and are rearranged into a pseudo sequence to be encoded by an video codec at encoder. Then the other unselected views are synthesized based on the similarity between neighboring views with our proposed method at decoder. To better characterize the non-linear relationship between the sub-views, a multi-branch spatial transformer networks (MSTN) is designed to adaptively learn the affine transformations between the neighboring views, which are used to warp the input views to generate accurate approximation of the target views. Moreover, to better obtain the final view by the generated approximation views, the Wasserstein generative adversarial networks(WGAN) is applied with the improved training. Experimental results show the superior compression performance of our scheme compared with the state-of-the-art methods.