In this paper, we consider the periodic boundary value problem with sign changing nonlinearity $$u^{{prime}{prime}{prime}}+{ ho}^3u=f(t,u),;t{in}[0,2{pi}]$$, subject to the boundary value conditions: $$u^{(i)}(0)=u^{(i)}(2{pi}),;i=0,1,2$$, where ${ ho}{in}(o,{frac{1}{sqrt{3}}})$ is a positive constant and f(t, u) is a continuous function. Using Leggett-Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The interesting point is the nonlinear term f may change sign.