<p>This paper addresses the distributed generalized Nash equilibrium (GNE) problem of multi-cluster games with coupling constraints, where only partial information is available. In this multi-cluster game, agents within each cluster cooperate to minimize the cluster’s objective function while ensuring that the strategies satisfy the coupling constraints. In our setup, each agent can only communicate with its neighboring agents via an undirected connected graph. To solve this GNE problem, we propose a distributed algorithm, which aims to achieve a variational GNE by appropriately selecting fixed step sizes. In the proposed algorithm, agents directly estimate the consensus strategy of each cluster without estimating the strategies of all other agents. It also eliminates the requirement for a centralized coordinator to collect and broadcast the total gradient of the cluster. With the help of operator theory, the proposed algorithm is expressed as a forward–backward iterative form represented by a pair of preconditioned operators, and its convergence is rigorously analyzed. Finally, the effectiveness and practical applicability of the designed algorithm are verified through an example in an energy system.</p>