With the large-scale integration of distributed generators (DGs), the coupling relations between transmission network (TN) and distribution networks (DNs) are getting closer. Coordinating the black-start processes of TN and DNs is beneficial to improving restoration efficiency. Therefore, a distributed black-start optimization method for global transmission and distribution (T&D) network is proposed in this paper. Firstly, a black-start optimization model of global T&D network is established to minimize the outage costs. Then, it is decomposed into the TN black-start optimization sub-problem and several DN black-start optimization sub-problems based on the analytical target cascading (ATC). The mixed integer quadratic programming (MIQP) is used for sub-problem modeling. The models take into account the restoration operations of different grid components at each black-start time step. The transmission control center (TCC) and distribution control centers (DCCs) only need to exchange partial information including the boundary power at each time step for distributed coordination, to obtain the coordinated black-start scheme for T&D network. Finally, the effectiveness of the proposed model and method is validated using a global T&D network case.