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 are operated on OFDMA systems, each subchannel can be reused separately among femtocells by carefully treating inter-cell interferences. 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 fmetocell networks, which make 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. Since the problem is formulated as a nonlinear integer programming, 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 femtocell to maximize the sum utility and finding actual subchannel allocation that achieves the granted number of subchannels for each femtocell. Numerical results show that the proposed subchannel allocation algorithm provides near-optimal performance.