Existing works on document image shadow removal mostly depend on learning and leveraging a constant background (the color of the paper) from the image. However, the constant background is less representative and frequently ignores other background colors, such as the printed colors, resulting in distorted results. In this paper, we present a color-aware background extraction network (CBENet) for extracting a spatially varying background image that accurately depicts the background colors of the document. Furthermore, we propose a background-guided document images shadow removal network (BGShadowNet) using the predicted spatially varying background as auxiliary information, which consists of two stages. At Stage I, a background-constrained decoder is designed to promote a coarse result. Then, the coarse result is refined with a background-based attention module (BAModule) to maintain a consistent appearance and a detail improvement module (DEModule) to enhance the texture details at Stage II. Experiments on two benchmark datasets qualitatively and quantitatively validate the superiority of the proposed approach over state-of-the-arts.