Fractional calculus theory shows unique advantage in aerodynamics, electrodynamics in complex medium, control theory, signal and image processing, rheology and many other issues. The study of such kind of problems has received considerable attention both in theory and applications.The investigation of fractional differential equations and their boundary value problems provide an important theoretical basis for the above problems.We consider the fractional differential equations with integral boundary conditions. First, we give the expression of the solution of the boundary value problem of the linear fractional differential equation, analyze the properties of the Green function, and give new estimate of a new upper bound of the Green function. Then by the Schauder fixed point theorem,we get the existence results of positive solution for the boundary value problems.