The deployment of small cells is one of the most effective means to cope with the traffic explosion of cellular mobile systems. However, a small cell system increases the inter-cell interference, which limits the capacity and degrades the cell-edge user throughput. Inter-cell interference coordination (ICIC), such as fractional frequency reuse (FFR), is a well-known scheme that autonomously mitigates inter-cell interference. In the Long Term Evolution (LTE)-Advanced, the three-dimensional (3D) beamforming, which combines conventional horizontal beamforming and vertical beamforming, has been gaining increasing attention. This paper proposes a novel centralized ICIC scheme that controls the direction of narrow 3D beam for each frequency band of each base station. The centralized controller collects information from the base stations and calculates sub-optimum combinations of narrow beams so as to maximize the proportional fair (PF) utility of all users. This paper describes the throughput of the new centralized ICIC scheme as evaluated by computer simulations and shows it has a significant gain in both average user throughput and cell-edge user throughput compared with the conventional ICIC scheme. This paper also investigates the feasibility of the scheme by assessing its throughput performance in a realistic deployment scenario.