A novel blind carrier frequency offset (CFO) estimation method for orthogonal frequency division multiplexing (OFDM) systems using constant modulus constellations is proposed in this study. CFO is estimated by minimizing a hybrid cost function which is formulated using properties of the covariance matrix and the magnitude of two nearby OFDM symbols. The performance of the proposed method is compared with that of the conventional estimation techniques under noisy time varying multipath channels. The performance comparison for different Doppler frequencies is also investigated. The superiority in performance of the proposed method over conventional methods is illustrated based on Monte Carlo simulations. © 2016 IEEE.