This paper is concerned with the following fourth-order four-point Sturm-Liouville boundary value problem $u^{(4)}(t)=f(t,;u(t),;u^{primeprime}(t))$, $0;{leq};t;{leq}1$, ${alpha}u(0)-{eta}u^{prime}(0)={gamma}u(1)+{delta}u^{prime}(1)=0$, $au^{primeprime}(xi_1)-bu^{primeprimeprime}(xi_1)=cu^{primeprime}(xi_2)+du^{primeprimeprime}(xi_2)=0$. Some sufficient conditions are obtained for the existence of at least one positive solution to the above boundary value problem by using the well-known Guo-Krasnoselskii fixed point theorem.