The present invention provides: a catalyst which has high activity and enables the production of an olefin polymer that has a polar group; and a method for producing the polymer. A catalyst for olefin polymerization, which contains a metal complex represented by general formula (C1); and a method for producing an ethylene (co)polymer, wherein (1) ethylene is polymerized, (2) ethylene and an olefin having a polar group represented by general formula (1) are copolymerized, or (3) ethylene, an olefin having a polar group represented by general formula (1) and another monomer are copolymerized, with use of the above-described catalyst. (In the formulae, the symbols are as defined in the description; and at least one of R6 and R7 represents a 9-fluorenyl analogous group represented by general formula (2).