We present a new algorithm for blind estimation of the symbol timing and frequency offset in a time-varying frequency-selective Rayleigh fading multipath channel for OFDM systems. It exploits the intrinsic structure of OFDM signals and only relies on a second-order moment without knowledge of the probability distribution function of the received signals. Under the minimum mean-square-error (MMSE) sense, the proposed estimators are totally optimum and easily implemented. Furthermore, we expand the estimation range of the frequency offset estimator and improve the timing estimator to be independent of the frequency offset. A more generalized channel model is considered. It is characterized by its power delay profile and time-varying scattering function. The channel has high reliability for a real mobile environment.