For an energy harvesting wireless network (EHWN), power oscillation will occur in uplink signal-to-interference-plus-noise ratio-based power control if some energy-non-supported nodes exist. Power oscillation will destroy power control algorithm's convergence and influence the system's stabilisation no matter the EHWN is feasible or infeasible. Unfortunately, existing algorithms cannot avoid the power oscillation. Therefore, the authors propose a new distributed algorithm which contains a soft removal mechanism to solve this problem in this study. Some energy harvesting nodes should be removed softly both in terms of their energy state information and channel state information. The convergence of the authors’ proposed algorithm can be guaranteed and power oscillation can be avoided in both feasible and infeasible EHWN. Simulation results verify their analysis and show that their algorithm brings less outage ratio than other algorithms.