Power systems are often seen as complex, nonlinear, dynamic systems with a variety inherent perturbation. Those operations may trigger steady-state instability in a power system, which may also result in the accumulation of poorly damped electromechanical modes or system collapse. To fix this problem, power system stabilizers are applied to generate extra excitation control system signals. Since gain settings are determined for the specific working conditions, a conventional power system stabilizer (CPSS) utilizes lead-lag compensation strategies. Fuzzy logic uses linguistic information and avoids complex mathematical models. A multi-level fuzzy-based power system stabilizer is addressed in this thesis to mitigate low-frequency oscillations in single and multi-machine power systems. The suggested controller uses the variation of rotor speed and acceleration as inputs. To show fuzzy controller performance, different membership functions, such as triangular, gaussian, generalized bell, and trapezoidal are taken. Electrical torque deviations using multi-level fuzzy with triangular, gaussian, and generalized bell membership function-based power system stabilizer reduce the settling time by 95.670 %, 55.961 %, and 2.231 % than a single fuzzy-based power system stabilizer. The multi-level fuzzy based PSS with triangular membership function reduced the settling time by 34.601 %, 27.030 %, and 95.670 % than single fuzzy-based PSS for rotor angle, rotor speed, and electrical torque deviations, respectively. The Multi-level Fuzzy based PSS with triangular membership function settled the rotor angle, rotor speed, and electrical torque deviations 29.517 %, 5.785 %, and 39.709 % faster than the gaussian membership function fuzzy-based PSS, respectively. When there is a 5 % change in both mechanical torque and reference voltage at a time in multi-machine system, a Multi-level Fuzzy based PSS achieved a settling time better than a single fuzzy-based power system stabilizer for machine-1, machine-2, and machine-3 for each state variable (power angle, rotor speed, and accelerating torque deviations). Triangular membership function resulted better result than the gaussian for single and multi-machine power system low frequency oscillation damping. Keywords: Low-Frequency Oscillation, Multi-Level Fuzzy, Multi-Machine, Power System Stabilizer