This paper studies the following Caputo fractional differential equation with p-Laplacian of higher-order multi-point： Dβ0+(_p(Dα0+u(t)))+f(t,u(t))=0,〓0≤t≤1,l-1<β≤l,n-1<α≤n,(_p(Dα0+u(0)))(i)=0,〓i=0,1,2,…,l-1,u(i)(0)=0,〓i=1,2,…,n-1,〓u(1)=∑ m-2 i=1 a_iu(ξ_i)。 Using the Schauder fixed point theorem, the existence of positive solution is obtained for the above boundary value problems. An example is presented to illustrate our main theorem.