The traditional blind signal to noise ratio (SNR) estimation algorithms for orthogonal frequency division multiplexing(OFDM) signals have the problems of poor performance and high computation complexity in low SNR and multi-path channel conditions. In order to treat these problems, a novel blind SNR estimation method for OFDM signals was proposed. Firstly, the AR model was established to estimate the power spectrum of the received observed signal. Secondly, the bandwidth was estimated by using second-order and fourth-order cumulants combined characteristic quantity and with jump edge extraction method. Finally, the SNR was estimated by calculating the in-band total power and the out-band noise power. The simulation results showed that the proposed method do not need any prior information and have better performance and lower computation complexity, which is more suitable for real-time non-cooperative communication systems.