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Imaging data-based prognostic models focus on using an asset’s degradation images to predict its time to failure (TTF). Most image-based prognostic models have two common limitations. First, they require degradation images to be complete (i.e., images are observed continuously and regularly over time). Second, they usually employ an unsupervised dimension reduction method to extract low-dimensional features and then use the features for TTF prediction. Because unsupervised dimension reduction is conducted on the degradation images without the involvement of TTFs, there is no guarantee that the extracted features are effective for failure time prediction. To address these challenges, this article develops a supervised tensor dimension reduction-based prognostic model. The model first proposes a supervised dimension reduction method for tensor data. It uses historical TTFs to guide the detection of a tensor subspace to extract low-dimensional features from high-dimensional incomplete degradation imaging data. Next, the extracted features are used to construct a prognostic model based on (log)-location-scale regression. An optimization algorithm for parameter estimation is proposed, and analytical solutions are discussed. Simulated data and a real-world data set are used to validate the performance of the proposed model. History: Bianca Maria Colosimo served as the senior editor for this article Funding: This work was supported by National Science Foundation [2229245]. Data Ethics & Reproducibility Note: The code capsule is available on Code Ocean at https://github.com/czhou9/Code-and-Data-for-IJDS and in the e-Companion to this article (available at https://doi.org/10.1287/ijds.2022.x022 ).