The presence of residual carrier frequency offset (CFO) in an orthogonal frequency division multiplexing (OFDM) system leads to a loss of orthogonality between the subcarriers. This introduces inter-subcarrier interference and degrades the system performance significantly. In the literature, Liu and Tureli proposed a blind CFO estimation method based on the observation that in a typical OFDM system not all the subcarriers are used for data transmission. However, the computational complexity of such a method is very high. Based on practical considerations, we propose an approximate closed-form solution for the blind estimation of CFO that is easily implementable at a very low cost. We also propose a successive CFO estimation and compensation procedure, which reduces the performance degradation of the proposed algorithm as compared with the method of Liu and Tureli when relatively large CFO values are assumed. In addition, a decision-directed extension of the successive algorithm, which further improves the CFO estimation at a slightly higher complexity, is also given.