Fractional calculus is widely used in fluid mechanics，electrochemical analysis，the electric conduction of biological systems and other fields. Boundary value problems of fractional differential equations has become a popular research and the problem in infinite interval is a difficult part. Aiming at these boundary value problems，this paper proposes a class of integral boundary problems of coupled fractional differential systems on infinite interval. By applying the properties of Green and conclusion of fractional calculus，the integral boundary problem of coupled fractional differential systems on infinite interval is transformed into equivalent integral system. By leading into product spaces，two-dimensional integral operators and using Krasnoselskii fixed point theorem on cone，some analytical skills，the sufficient condition of existence of at least one positive solution for the boundary value problem and new results of existence of positive solutions for integral boundary problem of coupled fractional differential systems on infinite interval are obtained.