Distributed optimal control problem with the constraint of fractional order diffusion equation is widely used in the description of scientific and engineering applications including optimal design, control and parameter identification. Aiming at this problem, a high-order fast algorithm is proposed. For the coupled two point boundary value problems arising from the first order optimality conditions for this problem, the problem is discretized in space by compact difference and in time by boundary value method. After discretization, a two-by-two block linear system is obtained. Then we use Kronecker product splitting preconditioning strategy for solving this linear system. The preconditioner is a bloc Kronecker product structure. We obtain this Kronecker product through an alternating Kronecker product splitting iteration method. We prove the convergence of this preconditioner algorithm and use GMRES method to accelerate the convergence of the Kronecker splitting iteration. Finally, numerical experiments show the accuracy and computational efficiency of the algorithm.