With a large amount of open satellite multispectral imagery (e.g., Sentinel-2 and Landsat-8), considerable attention has been paid to global multispectral land cover classification. However, its limited spectral information hinders further improving the classification performance. Hyperspectral imaging enables discrimination between spectrally similar classes but its swath width from space is narrow compared to multispectral ones. To achieve accurate land cover classification over a large coverage, we propose a cross-modality feature learning framework, called common subspace learning (CoSpace), by jointly considering subspace learning and supervised classification. By locally aligning the manifold structure of the two modalities, CoSpace linearly learns a shared latent subspace from hyperspectral-multispectral (HS-MS) correspondences. The multispectral out-of-samples can be then projected into the subspace, which are expected to take advantages of rich spectral information of the corresponding hyperspectral data used for learning, and thus leads to a better classification. Extensive experiments on two simulated HS-MS datasets (University of Houston and Chikusei), where HS-MS data sets have trade-offs between coverage and spectral resolution, are performed to demonstrate the superiority and effectiveness of the proposed method in comparison with previous state-of-the-art methods.