In this paper, we investigate resource block assignment in femtocell networks. A resource block assignment algorithm is designed to avoid co-channel intercell interference and ensure service quality for femtocell networks with dense and random femto deployments. We first formulate the optimization problem as the integer linear programming (ILP) on resource block assignment. The goal of the optimization formulation is to maximize the overall utilization of resource blocks with quality of service (QoS) constraints. We propose an efficient and simple algorithm termed interference-aware resource block assignment (IARBA). By considering conditions of resource blocks, the proposed approach achieves better resource block efficiency and assignment within QoS requirements. Our analytical and simulation results show that IARBA not only provides interference-free resource block assignment but also outperforms existing schemes in terms of average throughput with comparable complexities.