The classical Lie group analysis was used to obtain the corresponding infinitesimals of the seventh-order Kaup-Kupershmidt (KK) equation, and two different reduction equations were obtained. Many different forms of exact solutions of the seventh-order KK equation were achieved by solving the reduction equations, such as the rational function solution, the Jacobi elliptic function solution, the hyperbolic function solutions, the trigonometric function solutions and the power series solution, meanwhile, the convergence of the power series in the solution was proved.