In this paper, we propose an efficient carrier frequency offset (CFO) estimation technique based on the space alternating generalized expectation-maximization (SAGE) for uplink orthogonal frequency division multiple access (OFDMA) systems. In general, the SAGE method transforms a multidimensional search problem into a sequence of one-dimensional searches, which greatly simplifies the estimation procedure. However, the conventional algorithms based on the SAGE method require a large amount of computations to estimate the CFO due to exhaustive grid search. To reduce the computational burden, we exploit the leakage on the fast Fourier transform (FFT) output of the received signal after the multiple access interference is removed by the SAGE method. Then, this leakage-based approach reduces the complexity of the conventional SAGE algorithm regardless of an employed carrier assignment scheme by avoiding grid search. Simulation results show that our modified SAGE algorithm approaches the Cramer Rao bound at all signal to noise ratio (SNR) region with greatly reduced complexity compared to the conventional SAGE algorithms.