Although the distortion correction of fisheye images has been extensively studied, the correction of fisheye videos is still an elusive challenge. For different frames of the fisheye video, the existing image correction methods ignore the correlation of sequences, resulting in temporal jitter in the corrected video. To solve this problem, we propose a temporal weighting scheme to get a plausible global optical flow, which mitigates the jitter effect by progressively reducing the weight of frames. Subsequently, we observe that the inter-frame optical flow of the video is facilitated to perceive the local spatial deformation of the fisheye video. Therefore, we derive the spatial deformation through the flows of fisheye and distorted-free videos, thereby enhancing the local accuracy of the predicted result. However, the independent correction for each frame disrupts the temporal correlation. Due to the property of fisheye video, a distorted moving object may be able to find its distorted-free pattern at another moment. To this end, a temporal deformation aggregator is designed to reconstruct the deformation correlation between frames and provide a reliable global feature. Our method achieves an end-to-end correction and demonstrates superiority in correction quality and stability compared with the SOTA correction methods.