Screen content videos that typically contain computer generated texts and graphics are getting more demanding in nowadays online video service. They involve a great amount of circumstances that are not commonly seen in natural videos, including sharp edge transition and repetitive pattern, which make their statistical characteristics distinct from those of natural videos. This makes it questionable about the efficacy of the conventional discrete cosine transform (DCT), which builds on the Gauss-Markov model assumption that leads to a base-band signal, on coding the computer-generated graphics. This work exploits a class of staircase transforms. Unlike the DCT whose bases are samplings of sinusoidal functions, the staircase transforms have their bases sampled from staircase functions, which naturally better approximate the sharp transitions often encountered in the context of screen content. As an alternative transform kernel, the staircase transform is integrated into a hybrid transform coding scheme, in conjunction with DCT. It is experimentally shown that the proposed approach provides an average of 2.9% compression performance gains in terms of BD-rate reduction. A perceptual comparison further demonstrates that the use of staircase transform achieves substantial reduction in ringing artifact due to the Gibbs phenomenon.