One of the famous transformations is discrete cosine transform (DCT), which is always used in digital image coding standards like JPEG and MPEG. DCT has different types and all of DCTs have excellent energy compaction properties. Meanwhile, matrices of DCTs II and IV are examined by a lot of researchers. However, other types of DCTs are rarely developed. Therefore, this paper presents 4 × 4 parametric integer DCTs, which cannot only represent DCTs II and IV but other types of DCTs (i.e. DCT I, V, VIII). It shows an excellent performance in terms of mean square errors and transform coding gains while it is comparing with state of the art.