Cognitive Radio has attracted intensive interests of the researchers, recently. The data rate always increases in the emerging technologies. The increased data rate poses mainly two challenges for spectrum sensing. One is that the state of primary user (PU) is fast and alternatively varying between "on/off" in a spectrum sensing window. The other is that the asynchronicity among the reports in a cooperative spectrum sensing setting becomes more apparent. Both of them would deteriorate the spectrum sensing performance. Thus, we propose an asynchronous cooperative spectrum sensing method to cope with these two challenges. A likelihood ratio test based spectrum sensing is developed for a single cooperator. The likelihood ratio is obtained in the setting of fast varying PU state. The likelihood ratio test is uniformly powerful according to the Neyman-pearson lemma. Furthermore, the asynchronicity among the cooperators are studied. Two sets of fusion weights are discussed for the asynchronous time among cooperators. One is designed based on the condition probability of the PU state variation and the other one is designed based on the queueing theory. The simulation results are provided with different fusion methods. The performance improvements are demonstrated.