Hyperspectral tensor completion (HTC) for remote sensing, critical for advancing space exploration and other satellite imaging technologies, has drawn considerable attention from recent machine learning community. Hyperspectral image (HSI) contains a wide range of narrowly spaced spectral bands hence forming unique electrical magnetic signatures for distinct materials, and thus plays an irreplaceable role in remote material identification. Nevertheless, remotely acquired HSIs are of low data purity and quite often incompletely observed or corrupted during transmission. Therefore, completing the 3-D hyperspectral tensor, involving two spatial dimensions and one spectral dimension, is a crucial signal processing task for facilitating the subsequent applications. Benchmark HTC methods rely on either supervised learning or nonconvex optimization. As reported in recent machine learning literature, John ellipsoid (JE) in functional analysis is a fundamental topology for effective hyperspectral analysis. We therefore attempt to adopt this key topology in this work, but this induces a dilemma that the computation of JE requires the complete information of the entire HSI tensor that is, however, unavailable under the HTC problem setting. We resolve the dilemma, decouple HTC into convex subproblems ensuring computational efficiency, and show state-of-the-art HTC performances of our algorithm. We also demonstrate that our method has improved the subsequent land cover classification accuracy on the recovered hyperspectral tensor.