A class of boundary value problems for high order Riemann-Liouville fractional differential equation systems was studied. By the Laplace transform method, the integral expression of the boundary value problems was obtained. The existence theorem and the existence and uniqueness theorem for the solutions of the boundary value problems were established and proved by using the Leray-Schauder alternative and the Banach contraction mapping principle, respectively. Two examples were given to illustrate the main results.