A solid cocatalyst for olefin polymerization in which an ion-containing compound comprising a cation expressed by [R.sub.4M]+, wherein the group R are each individually selected from the group consisting of hydrogen atom and a substituted or non-substituted hydrocarbon group having from 1 to 30 carbon atoms with the exception of an aryl group; two or more groups R may form a ring by bonding with one another; at least one of the groups R is a hydrocarbon group having from 1 to 30 carbon atoms with the exception of an aryl group; and M represents nitrogen or sulfur, and a non-coordinating anion expressed by [A] said ion-containing compound is chemically bonded to a fine particulate carrier is used.