By using the symbolic computation software Maple,according to the concepts of single parameter invariant groups and group invariant solutions of differential equations,the general symmetry of the Hunter-Saxton equation was obtained with the help of its symmetry equation,which included five arbitrary constants and one arbitrary function.The Hunter-Saxton equation was reduced to some types of different ordinary differential equations by selecting different constants and function.Finally,with the transformational solving of the ordinary differential equations,group invariant solutions and exact solutions of the Hunter-Saxton equation were obtained directly.