This letter considers a multiple-channel cognitive radio network (CRN) which can simultaneously sense multiple narrowband channels at a time. Taking the maximization of the CRN's overall throughput as the design objective, the optimization problem of jointly designing sensing time, sensing thresholds and transmission power allocation is formulated under the total power constraint of the CRN and the average interference constraint of the primary network. An iterative algorithm is proposed to obtain the locally optimal values for these parameters. Finally, numerical results show that significant overall throughput gain is achieved through the joint design.