Femtocells provide high quality indoor communications with low transmit power. However, when femtocells are applied in cellular systems, a co-channel interference problem between macrocells and femtocells occurs because femtocells use the same spectrum as do the macrocells. To solve the co-channel interference problem, a previous study suggested a resource allocation scheme in LTE cellular systems using FFR. However, this conventional resource allocation scheme still has interference problems between macrocells and femtocells near the boundary of the sub-areas. In this paper, we define an optimization problem for resource allocation to femtocells and propose a femtocell resource allocation scheme to solve the optimization problem and the interference problems of the conventional scheme. The evaluation of the proposed scheme is conducted by System Level Simulation while varying the simulation environments. The simulation results show that the proposed scheme is superior to the conventional scheme and that it improves the overall performance of cellular systems.