Efficient and reliable spectrum sensing plays a critical role in cognitive radio networks. This paper presents a cooperative sequential detection scheme tominimize 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 average number of required samples depends on the Kullback-Leibler distance between the distributions of the two hypotheses under test. This suggests a criterion for selecting the most efficient radios to facilitate spectrum sensing. The paper also studies how to implement the scheme in a robust manner when the assumed statistical models have uncertainties. These ideas are illustrated through an example that assumes both the signal and noise are Gaussian distributed.