To provide varnish for infiltration-drying type offset ink used for a low class paper excellent in solving a problem of paper peeling in a high speed-printing of recent years, and the ink by using the varnish.

This varnish for the infiltration-drying type offset ink is provided by using a rosin-modified phenol resin having the molecular weight made as a high molecular weight of 70,000 to 1,200,000 not used conventionally as the varnish for the offset-printing ink and also having the dissolvability without forming turbidity in 10 to 35 wt.% solution of the varnish with a 15C aliphatic hydrocarbon at 25C. By using such the varnish as the penetration-drying offset-printing ink composition, especially on the high speed-printing, it becomes possible to satisfy printing aptitude excellent in solving the problem of the paper peeling.