The cat's eye resonator is designed with a cat's eye reflector as the resonator mirror. The configuration of the cat's eye reflector is described. The relation between the focal length of the cat's eye reflector and the distance between the convex lens and the concave mirror of the cat's eye reflector is indicated. Through controlling that distance in the cat's eye reflector, laser transverse mode is selected to ensure fundamental transverse mode output. In Newton-Cotes method based on the diffractive integral equation of the caser, laser transverse mode of the cat's eye cavity laser under variable parameters is analyzed. The eigenvalue ηmn and power loss which every transverse mode corresponds with are calculated. The parameter assuring fundamental transverse mode output obtained is well accordant to the experimental results. Therefore, a new convenient on-line means for the control and selection of the laser transverse mode is discovered.