Deformable registration between brain tumor images and brain atlas has been an important tool to facilitate pathological analysis. However, registration of images with tumors is challenging due to absent correspondences induced by the tumor. Furthermore, the tumor growth may displace the tissue, causing larger deformations than what is observed in healthy brains. Therefore, we propose a new reconstruction-driven cascade feature warping (RCFW) network for brain tumor images. We first introduce the symmetric-constrained feature reasoning (SFR) module which reconstructs the missed normal appearance within tumor regions, allowing a dense spatial correspondence between the reconstructed quasi-normal appearance and the atlas. The dilated multi-receptive feature fusion module is further introduced, which collects long-range features from different dimensions to facilitate tumor region reconstruction, especially for large tumor cases. Then, the reconstructed tumor images and atlas are jointly fed into the multi-stage feature warping module (MFW) to progressively predict spatial transformations. The method was performed on the Multimodal Brain Tumor Segmentation (BraTS) 2021 challenge database and compared with six existing methods. Experimental results showed that the proposed method effectively handles the problem of brain tumor image registration, which can maintain the smooth deformation of the tumor region while maximizing the image similarity of normal regions.