In this talk, a fractional optimal control problem with fractional Laplacian and integral state constraint is investigated. The first order optimality system and regularity of the solutions to optimal control problem are derived. Piecewise linear finite element method combined with variational discretization approach is used to approximate the optimal control problem. A priori error estimates for finite element approximation of the state, adjoint state and control variable are derived. Numerical examples are given to illustrate the theoretical findings.