The computational complexity of utility optimization for a large scale energy harvesting (EH) relay network is extremely high, especially when inputting finite-alphabet signals. This paper investigates the utility optimization for large scale EH relay networks with finite-alphabet inputs by the stable matching scheme. First, we divide the nodes, which may act as a user or a relay, into multiple clusters, and perform optimization strategy within the clusters. Second, the optimal power bought from the relay node to maximize the utility of the user is derived. Then, the mutual preference matrices between the users and relays by the maximum utility criterion are established. Base on the mutual preference matrices, an improved Gale-Shapley (GS) algorithm is proposed to get a sub-optimal result. The simulation results demonstrate that the proposed algorithm can bring significant performance improvements and achieve higher energy efficiency compared with the conventional algorithms. In contrast to the exhausted Search (ES) method, it costs much less time and accomplishes an approximative utility output. Moreover, the proposed scheme incurs low signaling overhead which makes it practical to be implemented. INDEX TERMS Large scale relay networks, utility optimization, stable matching, finite-alphabet inputs, energy harvesting.