In femtocell networks, due to their small cell size, we can achieve higher spatial diversity from the channel reuse between multiple femtocells. In addition, if femtocells operate on OFDMA systems, each subchannel can be reused separately among femtocells, improving system efficiency more significantly. However, due to a large number of femtocells and their uncoordinated and irregular deployment, we need to treat intercell interferences very carefully in OFDMA-based femtocell networks, which makes developing efficient resource allocation schemes more difficult.In this paper, we study a subchannel allocation problem that aims at maximizing the sum utility of the OFDMA-based femtocell network, which can be applied to both the dedicated channel and shared channel femtocell deployments. Since the problem is formulated as a nonlinear integer program, which is inherently difficult to solve, we propose a suboptimal subchannel allocation algorithm. The proposed subchannel allocation algorithm consists of two steps: calculating the number of subchannels that should be granted to each cell to maximize the sum utility and finding actual subchannel allocation that achieves the granted number of subchannels for each cell. Numerical results show that the proposed subchannel allocation algorithm provides near-optimal performance.