Recent research has shown that integer cosine transforms (ICTs) can avoid some mismatches of discrete cosine transform (DCT) and improve the efficiency of image compression. Furthermore, ICTs with different sizes can be implemented in numerous fields. For example, the larger transforms can improve the transform coding performance in high-definition videos, such as the size of 16×16. This paper generates a technique of parametric integer cosine transform (PICT), which owns the flexibilities of choosing separate integer parameters and different sizes including 16-order. This strategy also has a simple structure based on the matrix factorization, which only contains the integer operation. The proposed ICT can lead to a higher coding gain and peak signal-to-noise ratio performance as well as closer to the original discrete cosine transform than state of the art.