Wideband spectrum sensing has drawn much attention in recent years since it provides more opportunities to the secondary users. However, wideband spectrum sensing requires a long time and a complex mechanism at the sensing terminal.A two-stage wideband spectrum sensing scheme is considered to proceed spectrum sensing with low time consumption and high performance to tackle this predicament. In this scheme, a novel multitaper spectrum sensing(MSS) method is proposed to mitigate the poor performance of energy detection(ED) in the low signal-to-noise ratio(SNR) region. The closed-form expression of the decision threshold is derived based on the Neyman–Pearson criterion and the probability of detection in the Rayleigh fading channel is analyzed. An optimization problem is formulated to maximize the probability of detection of the proposed two-stage scheme and the average sensing time of the two-stage scheme is analyzed. Numerical results validate the efficiency of MSS and show that the two-stage spectrum sensing scheme enjoys higher performance in the low SNR region and lower time cost in the high SNR region than the single-stage scheme. Wideband spectrum sensing has drawn much attention in recent years since it provides more opportunities to the secondary users. However, wideband spectrum sensing requires a long time and a complex mechanism at the sensing terminal. A two-stage wideband spectrum sensing scheme is considered to proceed spectrum sensing with low time consumption and high performance to tackle this predicament. In this scheme, a novel multitaper spectrum sensing (MSS) method is proposed to mitigate the poor performance of energy detection (ED) in the low signal-to-noise ratio SNR) region. The closed-form expression of the decision threshold is derived based on the Neyman-Pearson criterion and the probability of detection in the Rayleigh fading channel is analyzed. An optimization problem is formulated to maximize the probability of detection of the proposed two -stage scheme and the average sensing time of the two-stage scheme are analyzed. Numerical results validate the efficiency of MSS and show that the t wo-stage spectrum sensing scheme entitled higher performance in the low SNR region and lower time cost in the high SNR region than the single-stage scheme.