In this paper, we propose a low-complexity blind carrier frequency offset (CFO) estimation scheme, for constant modulus (CM) signaling based orthogonal frequency division multiplexing (OFDM) systems. Provided that the channel can be assumed to be slowly time-varying, subcarriers having the same indices in two consecutive OFDM symbols will experience nearly the same channel effect. This assumption enables us to derive a cost function that is determined by the sum of the products of the signal amplitudes on each pair of equivalent subcarriers from two successive OFDM symbols. The maximization process of this cost function makes it possible to find an appropriate estimate of the CFO. Over frequency-selective Rayleigh fading channels, the proposed CFO estimation method provides improved performance over existing techniques. Moreover, in contexts of narrowband noise and signal gain variations, simulations demonstrate the robustness and immunity of our scheme.