Co-clustering aims to simultaneously cluster the objects and features to explore intercorrelated patterns. However, it is usually difficult to obtain good co-clustering results by just analyzing the object-feature correlation data due to the sparsity of the data and the noise. Meanwhile, most co-clustering algorithms cannot take the prior information into consideration and may produce unmeaningful results. Semi-supervised co-clustering aims to incorporate the known prior knowledge into the co-clustering algorithm. In this paper, a new technique named constraint co-projections for semi-supervised co-clustering (CPSSCC) is presented. Constraint co-projections can not only make use of two popular techniques including pairwise constraints and constraint projections, but also simultaneously perform the object constraint projections and feature constraint projections. The two popular techniques are illustrated for semi-supervised co-clustering when some objects and features are believed to be in the same cluster a priori. Furthermore, we also prove that the co-clustering problem can be formulated as a typical eigen-problem and can be efficiently solved with the selected eigenvectors. To the best of our knowledge, constraint co-projections is first stated in this paper and this is the first work on using CPSSCC. Extensive experiments on benchmark data sets demonstrate the effectiveness of the proposed method. This paper also shows that CPSSCC has some favorable features compared with previous related co-clustering algorithms.