The method of combining function transformations with auxiliary equation is presented to search for new infinite sequence soliton-like solutions of Camassa-Holm-r (CH-r) equation. And many new conclusions are obtained. Step one,according to some function transformations, CH-r equation is changed into the solvable ordinary differential equation. Step two, new infinite sequence soliton-like solutions of CH-r equation are constructed by applying new solutions and Bäcklund transformation of the solvable ordinary differential equation.