Collective matrix completion refers to the problem of simultaneously predicting the missing entries in multiple matrices by leveraging the cross-matrix information. It finds abundant applications in various domains such as recommender system, dimensionality reduction, and image recovery. Most of the existing work represents the cross-matrix information in a shared latent structure constrained by the Euclidean-based pairwise similarity, which may fail to capture the nonlinear relationship of the data. To address this problem, in this paper, we propose a new collective matrix completion framework, named C4, which uses the graph spectral filters to capture the non-Euclidean cross-matrix information. To the best of our knowledge, this is the first effort to represent the cross-matrix information in the graph spectral domain. We benchmark our model against 8 recent models on 10 real-world data sets, and our model outperforms state-of-the-art methods in most tasks.