This paper describes the optimization of spectrum sensing in terms of the throughput of a cognitive radio (CR) system. Dealing with the optimization problem of spectrum sensing, this paper evaluates the throughput of a CR system by considering such situations as the penalty time of a channel search and incumbent user (IU) detection delay caused by a missed detection of an incumbent signal. Also, this paper suggests a serial channel search scheme as the search method for a vacant channel, and derives its mean channel search time by considering the penalty time due to the false alarm of a vacant channel search. The numerical results suggest the optimum sensing time of the channel search process using the derived mean channel search time of a serial channel search in the case of a sensing hardware structure with single radio frequency (RF) path. It also demonstrates that the average throughput is improved by two separate RF paths in spite of the hardware complexity of an RF receiver.