Efficient and reliable spectrum sensing plays a critical role in cognitive radio networks. This paper presents a cooperative sequential detection scheme to reduce the average sensing time that is required to reach a detection decision. In the scheme, each cognitive radio computes the log-likelihood ratio for its every measurement, and the base station sequentially accumulates these log-likelihood statistics and determines whether to stop making measurement. The paper studies how to implement the scheme in a robust manner when the assumed signal models have unknown parameters, such as signal strength and noise variance. These ideas are illustrated through two examples in spectrum sensing. One assumes both the signal and noise are Gaussian distributed, while the other assumes the target signal is deterministic.