The present invention provides method of preparing alkene-acrylate-norbornene terpolymer by polymerization of a monomer mixture consisting of alkene, acrylate and norbornene by a radical initiator under the presence of a Lewis acid.In the method of preparing the alkene-acrylate-norbornene terpolymer of the present invention, the terpolymer may be prepared in the mild condition of low temperature and low pressure by using the Lewis acid so that the process is simple and the property of the terpolymer may be easily controlled. In addition, the terpolymer prepared by the method includes the ethylene and the norbornene simultaneously so that it has high glass transition temperature, and the brittle property in forming of film is improved.