Applying image-based processing methods to original videos on a framewise level breaks the temporal consistency between consecutive frames. Traditional video temporal consistency methods reconstruct an original frame containing flickers from corresponding nonflickering frames, but the inaccurate correspondence realized by optical flow restricts their practical use. In this article, we propose a temporally broad learning system (TBLS), an approach that enforces temporal consistency between frames. We establish the TBLS as a flat network comprising the input data, consisting of an original frame in an original video, a corresponding frame in the temporally inconsistent video on which the image-based technique was applied, and an output frame of the last original frame, as mapped features in feature nodes. Then, we refine extracted features by enhancing the mapped features as enhancement nodes with randomly generated weights. We then connect all extracted features to the output layer with a target weight vector. With the target weight vector, we can minimize the temporal information loss between consecutive frames and the video fidelity loss in the output videos. Finally, we remove the temporal inconsistency in the processed video and output a temporally consistent video. Besides, we propose an alternative incremental learning algorithm based on the increment of the mapped feature nodes, enhancement nodes, or input data to improve learning accuracy by a broad expansion. We demonstrate the superiority of our proposed TBLS by conducting extensive experiments.