To solve the power supply problem of battery-limited Internet of Things devices (IoDs) and the spectrum scarcity problem, simultaneous wireless information and power transfer (SWIPT) and cognitive radio(CR) technology were integrated into the Internet of Things (IoT) network to build a cognitive radio IoT (CRIoT) with SWIPT. In this network, secondary users (SUs) could adaptively switch between spectrum sensing, SWIPT, and information transmission to improve the total throughput. To solve the complicated multi-dimensional resource allocation problem in CRIoT with SWIPT, we propose a multi-dimensional resource allocation algorithm for maximizing the total throughput. Three-dimensional resources were jointly optimized, which are time resource (the duration of each process), power resource (the transmit power and the power splitting ratio of each node), and spectrum resource, under some constraints, such as maximum transmit power constraint and maximum permissible interference constraint. To solve this intractable mixed-integer nonlinear program (MINLP) problem, firstly, the sensing task assignment for cooperative spectrum sensing (CSS) was obtained by using a greedy sensing algorithm. Secondly, the original problem was transformed into a convex problem via some transformations with fixed-power splitting ratio and time switching. The Lagrange dual method and subgradient method were adopted to obtain the optimal power and channel allocation. Then, a one-dimensional search algorithm was used to obtain the optimal power splitting ratio and the time switching ratio. Finally, a heuristic algorithm was adopted to obtain the optimal sensing duration. The simulation results show that the proposed algorithm can achieve higher total system throughput than other benchmark algorithms, such as a greedy algorithm, an average algorithm, and the Kuhn–Munkres (KM) algorithm.