The cooperative device-to-device (D2D) system is becoming one of the most popular communication models in wireless 5G technology that combines the D2D system with cooperative communication to extend coverage and increase system performance. However, interference is one of the factors of decreasing service quality in cooperative D2D systems because of adjacent users/clusters and excessive power usage, which also causes interference to the receiver. Interference management, such as power control, can overcome interference problems in the cooperative D2D communication system. Therefore, this paper proposes a new form of adaptive power control (APC) based on the low-energy adaptive clustering hierarchy (LEACH) protocol for interference management systems in cooperative D2D systems that other studies have not considered. For a fair comparison, this paper also modifies the conventional fixed power control (FPC) method using the LEACH protocol and the modified fixed power control (MFPC) used in the previous study and then considers the system without power control. The simulation results show that the proposed APC can significantly reduce interference in cooperative D2D communication compared to the MFPC and without power control. Moreover, the simulation results also show that concerning the signal-to-interference and noise ratio (SINR) to the outage probability and throughput, the proposed APC performs better than the MFPC and without power control. Thus, the proposed APC can effectively reduce interference in cooperative D2D systems.