Maximum likelihood (ML) carrier-frequency offset estimation for orthogonal frequency-division multiple access uplink is a complex multi-parameter estimation problem. The ML approach is a global optima search problem, which is prohibitive for practical applications because of the requirement of multidimensional exhaustive search for a large number of users. There are a few attempts to reduce the complexity of ML search by applying evolutionary optimisation algorithms. In this study, the authors propose a novel canonical particle swarm optimisation (CPSO)-based scheme, to reduce the computational complexity without compromising the performance and premature convergence. The proposed technique is a two-step process, where, in the first step, low resolution alternating projection frequency estimation (APFE) is used to generate a single better positioned particle for CPSO, followed by an actual CPSO procedure in second step. The mean square error performance of the proposed scheme is compared with existing low complexity algorithms namely APFE and linear particle swarm optimisation with mutation. Simulation results presented in this study show that the new scheme completely avoids premature convergence for a large number of users as high as 32.