In this paper we propose a novel resource allocation scheme to achieve a balanced performance improvement for all users in a LTE network subject to inter-cell interference. In the proposed scheme the resource allocation process is implemented in two steps. In the first step interference coordination and scheduling are first conducted in a global manner to prevent cell-edge users from mutual interference. In the second step, optimal power allocation is conducted to maximize performance of cell-edge users while maintaining high performance of cell-center users. The optimal power allocation problem is solved using the Lagrange decomposition method. Simulation results show that our proposed scheme can significantly improve performance for all users in a multi-cell network and achieve a better performance balance between cell-edge and cell-center users.