Spectrum sensing in a cognitive radio network involves detecting when a primary user vacates their licensed spectrum, to enable secondary users to broadcast on the same band. Accurately sensing the absence of the primary user ensures maximum utilization of the licensed spectrum and is fundamental to building effective cognitive radio networks. In this paper, we address the issues of enhancing sensing gain, average throughput, energy consumption, and network lifetime in a cognitive radio-based Internet of things (CR-IoT) network using the non-sequential approach. As a solution, we propose a Dempster–Shafer theory-based throughput analysis of an energy-efficient spectrum sensing scheme for a heterogeneous CR-IoT network using the sequential approach, which utilizes firstly the signal-to-noise ratio (SNR) to evaluate the degree of reliability and secondly the time slot of reporting to merge as a flexible time slot of sensing to more efficiently assess spectrum sensing. Before a global decision is made on the basis of both the soft decision fusion rule like the Dempster–Shafer theory and hard decision fusion rule like the “n-out-of-k” rule at the fusion center, a flexible time slot of sensing is added to adjust its measuring result. Using the proposed Dempster–Shafer theory, evidence is aggregated during the time slot of reporting and then a global decision is made at the fusion center. In addition, the throughput of the proposed scheme using the sequential approach is analyzed based on both the soft decision fusion rule and hard decision fusion rule. Simulation results indicate that the new approach improves primary user sensing accuracy by 13% over previous approaches, while concurrently increasing detection probability and decreasing false alarm probability. It also improves overall throughput, reduces energy consumption, prolongs expected lifetime, and reduces global error probability compared to the previous approaches under any condition [part of this paper was presented at the EuCAP2018 conference (Md. Sipon Miah et al. 2018)].