This paper investigates the distributed strategy design to find generalized Nash equilibria (GNE) of multi-cluster games with nonsmooth payoff functions, a coupled nonlinear inequality constraint, and set constraints. In this game, each cluster is composed of a group of agents and is a virtual noncooperative player, who minimizes its payoff function; each agent only uses its local payoff function, local feasible set and partial information of the coupled inequality constraint, and communicates with its neighbors. To solve the GNE problem, we propose a distributed nonsmooth algorithm using a projected differential inclusion and establish the convergence analysis of the proposed algorithm. A numerical application is given for illustration. (C) 2019 Elsevier Ltd. All rights reserved.