This paper describes a design procedure for a Grey ANFIS based power system stabilizer (GrANFIS-PSS) and investigates their robustness for a multi-machine power system. Speed deviation of a machine and its derivative are chosen as the input signals to the GrANFIS-PSS. A four-machine and a two-area power system is used as the case study. Computer simulations for the test system subjected to transient disturbances i.e. a three phase fault, were carried out and the results showed that the proposed controller is able to prove its effectiveness and improve the system damping when compared to a conventional lead-lag based power system stabilizer controller. The simulation result shows that the GrANFIS-PSS can be designed to achieve good performance merely using the combination of Grey prediction and Adaptive Neuro-Fuzzy Inference System (ANFIS). GrANFIS-PSS is designed to damp out the low frequency local and inter-area oscillations of the Multi-machine power system. By applying this GrANFIS-PSS to the power system the damping of inter-area modes of oscillations in a multi-machine power system is handled properly. The effectiveness of the proposed GrANFIS-PSS is demonstrated on two area four machine power system (Kundur system), which has provided a comprehensive evaluation of the learning control performance. Finally, several fault and load disturbance simulation results are presented to stress the effectiveness of the proposed GrANFIS-PSS in a multimachine power system and show that the proposed intelligent controls improve the dynamic performance of the GrANFIS-PSS and the associated power network