In this paper, we propose a practically efficient Subcarrier Allocation scheme based on Lagrangian relaxation to solve the problem of subcarrier allocation in OFDMA wireless channels. The problem of subcarrier allocation is formulated into an Integer Programming (IP) problem, which is relaxed by replacing complicating constraints with Lagrange multipliers using Lagrangian Relaxation. A subgradient method is used to optimize the Lagrangian dual function and a heuristic is designed to obtain the feasible solution. Lagrangian Relaxation Subcarrier Allocation (LRSA) is proven to be of polynomial complexity and it provides bounds on the value of channel efficiency. Numerical results show that compared with other algorithms proposed in the literature, LRSA can result in a significant improvement in channel efficiency, while at the same time guaranteeing minimum data rates of users.