This paper studies the problem of optimal control with state constraints for mean-field type stochastic systems, which is governed by fully coupled forward-backward stochastic differential equations(FBSDE) with Teugels martingales. In this system, the coefficients contain not only the state processes but also its marginal distribution, and the cost function is of mean-field type as well. We use an equivalent backward formulation to deal with the terminal state constraint, and then we obtain a stochastic maximum principle by Ekeland’s variational principle. In addition, we discuss a stochastic LQ control problem with state constraints.