Internet of Things (IoT) is able to provide various physical objects to exchange their information through the 6G wireless communication network. However, with the large increasing number of the IoT devices (IoDs), the deployment of IoDs faces two basic challenges, i.e., spectrum scarcity and energy limitation. Cooperative spectrum sharing and simultaneous wireless information and power transfer (SWIPT) provide effective ways to improve the spectrum and energy efficiency. In this article, two SWIPT cooperative spectrum sharing methods are proposed to improve the energy and spectrum efficiency for 6G-enabled cognitive IoT network, in which IoDs access to the primary spectrum by serving as orthogonal frequency-division multiplexing (OFDM) relay with the energy harvested from the received radio-frequency (RF) signal. Specifically, in phase1, the IoDs transmitter (DT) in the cognitive IoT network performs information decoding and energy harvesting with the received RF signal. In phase2, DT transmits the signals of the primary system and itself to the corresponding receiver by utilizing orthogonal subcarriers with the harvested energy to avoid the interference. Achievable rates of the cognitive IoT system with amplify-and-forward (AF) and decode-and-forward (DF) relaying mode are maximized through joint power and subcarrier optimization, while ensuring the target rate of the primary system. Simulation results are performed to illustrate the improvement of the spectrum and energy efficiency.