Currently, there is a growing demand for the use of communication network bandwidth for the Internet of Things (IoT) within the cyber-physical-social system (CPSS), while needing progressively more powerful technologies for using scarce spectrum resources. Then, cognitive radio networks (CRNs) as one of those important solutions mentioned above, are used to achieve IoT effectively. Generally, dynamic resource allocation plays a crucial role in the design of CRN-aided IoT systems. Aiming at this issue, orthogonal frequency division multiplexing (OFDM) has been identified as one of the successful technologies, which works with a multi-carrier parallel radio transmission strategy. In this article, through the use of swarm intelligence paradigm, a solution approach is accordingly proposed by employing an efficient Jaya algorithm, called PA-Jaya, to deal with the power allocation problem in cognitive OFDM radio networks for IoT. Because of the algorithm-specific parameter-free feature in the proposed PA-Jaya algorithm, a satisfactory computational performance could be achieved in the handling of this problem. For this optimization problem with some constraints, the simulation results show that compared with some popular algorithms, the efficiency of spectrum utilization could be further improved by using PA-Jaya algorithm with faster convergence speed, while maximizing the total transmission rate.