The present invention relates to a covalent organic framework which is a two-dimensional polymer formed by repeatedly arranging structural units represented by formula I or formula II and bonding same by means of covalent bonds. The present invention also relates to a catalyst, preparation methods for the covalent organic framework and the catalyst, and applications of the covalent organic framework and the catalyst in catalyzing olefin polymerization. The covalent organic framework can be used as a support to control the stereoregular polymerization of olefins in a confined space. The catalyst has high catalytic activity and good high-temperature stability, and widens the range of types of olefin polymerization catalysts.