Orthogonal frequency division multiple access (OFDMA) is a promising technique, which can provide high downlink capacity for future wireless systems. The total capacity of OFDMA can be maximized by adaptively assigning subchannels to the user with the best gain for that subchannel, with power subsequently distributed by water-filling algorithm. In this paper we have proposed the use of a customized particle swarm optimization (PSO) aided algorithm to allocate the subchannels. The PSO algorithm is population-based: a set of potential solutions evolves to approach a near-optimal solution for the problem under study. The customized algorithm works for discrete particle positions unlike the classical PSO algorithm which is valid for only continuous particle positions. It is shown that the proposed method obtains higher sum capacities as compared to that obtained by previous works, with comparable computational complexity.