In this paper, we propose a simple frequency offset estimation (FOE) algorithm for high-speed coherent optical orthogonal frequency-division multiplexing (CO-OFDM) systems, which avoids the exhaustive search computations on the integer part of FOE by using a merit function. In time domain, the FOE algorithm can estimate all the frequency offset in the range of [-5GHz, +5GHz], for satisfying the practical application requirement, based on only one redesigned training symbol. In addition, we provide the theoretical analysis about the quantitative influences of the residual frequency offset (RFO) on CO-OFDM systems. In order to reduce the final estimation error, a new zero-overhead residual frequency offset estimation (RFOE) algorithm is also proposed in this paper. Finally, the feasibility and effectiveness of the proposed FOE and RFOE algorithms are demonstrated in a 464 Gbit/s polarization-division multiplexed (PDM) 16-ary quadrature amplitude modulation (QAM) CO-OFDM system by the simulation, and numerical results validate the proposed algorithms.