To obtain a high performance preliminary polymerized solid catalyst and to provide a method for preparing the preliminary polymerized solid catalyst and a heterogeneous polymerization system capable of stably performing the heterogeneous polymerization of an olefin.

This preliminary polymerized solid catalyst is prepared by polymerizing an olefin under the irradiation of an elastic wave on an olefin polymerization catalyst in a heterogeneous system. In the presence of the preliminary polymerized solid catalyst, ≥0.1g olefin is preliminary polymerized based on 1mmol transition metal in the olefin polymerization catalyst. The flexible wave is preferably and concretely an ultrasonic wave. In the presence of the preliminary polymerized solid catalyst, the olefin is polymerized in a slurry or in a gas phase. It is also preferable that the polyolefin may be produced by polymerizing the olefin under the irradiation of the elastic wave in the heterogeneous system, in the presence of the olefin polymerization catalyst.