This article describes the application of a new population-based meta-heuristic optimization algorithm inspired by the kidney process in the human body for the tuning of power system stabilizers (PSSs) in a multi-machine power system. The tuning problem of PSS parameters is formulated as an optimization problem that aims at maximizing the damping ratio of the electromechanical modes and the kidney-inspired algorithm (KA) is used to search for the optimal parameters. The efficacy of the KA-based PSS design was successfully tested on a well-known 16-machine, 68-bus power system. The obtained results are evaluated and compared with the other results obtained by the original particle swarm optimization (PSO) and the bat algorithm (BA) methods. From the detailed eigenvalue analysis, the nonlinear simulation studies and some performance indices it has been found out that for damping oscillations, the performance of the proposed KA approach in this study is better than that obtained by other intelligent techniques (PSO and BA). Moreover, the efficiency and the superior performance of the proposed method over the other two algorithms in terms of computation time, convergence rate and solution quality are confirmed.