The cognitive sensor (CS) can transmit data to the control center in the same spectrum that is licensed to the primary user (PU) when the absence of the PU is detected by spectrum sensing. However, the battery energy of the CS is limited due to its small size, deployment in atrocious environments and long-term working. In this paper, an energy-harvesting-based CS is described, which senses the PU together with collecting the radio frequency energy to supply data transmission. In order to improve the transmission performance of the CS, we have proposed the joint resource allocation of spectrum sensing and energy harvesting in the cases of a single energy-harvesting-based CS and an energy-harvesting-based cognitive sensor network (CSN), respectively. Based on the proposed frame structure, we have formulated the resource allocation as a class of joint optimization problems, which seek to maximize the transmission rate of the CS by jointly optimizing sensing time, harvesting time and the numbers of sensing nodes and harvesting nodes. Using the half searching method and the alternating direction optimization, we have achieved the sub-optimal solution by converting the joint optimization problem into several convex sub-optimization problems. The simulation results have indicated the predominance of the proposed energy-harvesting-based CS and CSN models.