An isobutylene-based polymer as a polymer of cationically polymerizable monomers principally composed of isobutylene or a combination of isobutylene and a styrene-series monomer, generates a molded article with outstanding properties, the isobutylene-based polymer characteristically satisfying the following provisions; 1. the isobutylene-based polymer has a substantially continuos molecular weight distribution on a gel-permeation chromatogram; 2. the molecular weight at the highest peak on a gel-permeation chromatogram is within a range of 10,000 to 500,000; and 3. the length (a) of the elution time in the lower molecular region of the mountain from the highest peak and the length (b) of the elution time in the higher molecular region of the mountain from the highest peak on a gel-permeation chromatogram, satisfy the provision represented by the formula (b)/(a).gtoreq.1.3.