The paper deals with a class of time-inconsistent control problems for McKean-Vlasov dynamics. By solving a backward equilibrium Hamilton-Jacobi-Bellman equation coupled with a forward distribution-dependent stochastic differential equation, we investigate the existence and uniqueness of a closed-loop Makovian equilibrium for such time-inconsistent distribution-dependent control problem. Moreover, a special case of semilinear McKean-Vlasov dynamics with a quadratic-type cost functional is considered due to its special structure.