In this paper, we investigate the features of energy detection and cyclostationary feature detection for spectrum sensing. In order to combine their advantages, we propose an adaptive two-stage sensing scheme which performs spectrum sensing using an energy detector first in cognitive radio networks. Then in the second stage, this scheme decides whether or not to implement cyclostationary feature detection based on the sensing results of the first stage. On the premise of meeting a given constraint on the probability of false alarm, the goal of our proposed scheme is to optimize the probability of detection and sensing speed at the same time. In order to obtain the optimal detection thresholds, we can formulate the detection model as a nonlinear optimization problem. Furthermore, the simulation results show that the proposed scheme improves the performance of spectrum sensing compared with the ones where only energy detection or cyclostationary feature detection is performed.