The non-zero carrier frequency offset (CFO) must be compensated for orthogonal frequency-division multiplexing (OFDM) communications since it may destroy the orthogonality among subcarriers and cause severe degradation in system performance. Several blind CFO estimation methods were developed by exploiting the virtual carriers in practical OFDM transmissions, including a highly efficient approach by rooting a polynomial. However, this rooting method is suboptimal when the noise is present. In this work, we propose an improved polynomial rooting method that is shown to be the maximum likelihood (ML) estimator for both the noisy and the noise-free case. The simulation results clearly show the effectiveness and the better performance of the newly proposed method