Abstract: This paper deals with frame detection of OFDM signal with multiple-periodic preambles transmitted over frequency-selective channels and with existence of carrier fre-quency offset. Involving effect of AGC (Automatic Gain Control), frame detection can be taken as a hypothesis test model with unknown parameters. By applying generalized log-likelihood ratio testing to this model, a simple CFAR (Constant False-Alarm Rate) detector that is insensitive to frequency offset is derived. Parametric generalized lambda distribution is utilized to fit the statistical characteristic of detector when only noise exists, which is then used by Neyman-Pearson rule to determine decision threshold at given false alarm proba-bility. Finally, computer simulations achieve detection performance of the obtained frame detector.