Environmental noises greatly degrade the performance of speaker verification system. This paper designs a novel noise-robust speaker verification system based on multi- SNR techniques using 1/f\alpha noises. During training phase, the 1/f\alpha noises are employed to simulate environmental noises. To simplify the computation load, an optimal value of a is selected. To evaluate the performance of the system, speaker verification experiments are conducted on 5 kinds of environmental noises: "airport", "bus", "lobby", "restaurant", and "office" at 0dB SNR. The experimental results demonstrate that a notable degradation of verification error rates is obtained while using 1/f\alpha noises.