In daily photography, it is common to capture images in the reflection of an unwanted scene. This circumstance arises frequently when imaging through a semi-reflecting material such as glass. The unwanted reflection will affect the visibility of the background image and introduce ambiguity that perturbs the subsequent analysis on the image. It is a very challenging task to remove the reflection of an image since the problem is severely ill-posed. In this paper, we propose a novel algorithm to solve the reflection removal problem based on light field (LF) imaging. For the proposed algorithm, we first show that the strong gradient points of an LF epipolar plane image (EPI) are preserved after adding to the EPI of another LF image. We can then make use of these strong gradient points to give a rough estimation of the background and reflection. Rather than assuming that the background and reflection have absolutely different disparity ranges, we propose a sandwich layer model to allow them to have common disparities, which is more realistic in practical situations. Then, the background image is refined by recovering the components in the shared disparity range using an iterative enhancement process. Our experimental results show that the proposed algorithm achieves superior performance over traditional approaches both qualitatively and quantitatively. These results verify the robustness of the proposed algorithm when working with images captured from real-life scenes.