This paper presents a Genetic Algorithm for Power System Stabilizers (GAPSS) design in a multi-machine power system. The proposed GAPSS is to find the best location and optimal parameters of the power system stabilizers (PSS) in order to improve the dynamic and transient stability of a power system over a wide range of operating conditions. The objective function allows the selection of the stabilizer parameters to shift critical closed loop eigenvalues to the left-hand side the complex S plane. Simulation studies are performed to demonstrate the effectiveness of the GAPSS under different operating conditions and disturbances.