Abstract: The detection time required to reach a decision in sequential detection is a random variable. Although the sequential detection has a high average detection speed, very long detection time may be required in some specific cases. In order to improve the speed of spectrum sensing as well as to avoid some too-long-sensing-time tests in cognitive radio, a truncated sequential detection algorithm is proposed. Firstly, the effect of truncation on the performance of conventional sequential detection is analyzed, and the upper bounds of the false alarm and the miss detection probability are derived. Then the detection thresholds of truncated sequential detection are derived based on the upper bounds. Finally, the process of the truncated sequential detection algorithm is proposed. The simulation results show that the proposed algorithm, under the constraint of limited sensing time, can satisfy the performance requirement, and still have a shorter average sensing time than the conventional energy detection does.