The power quality is becoming an extensively addressing aspect of power system because of sensitive operation of smart grid, awareness of power quality and modern power system equipment. This paper proposes a new hybrid algorithm of Advanced Gravitational Search Algorithm-based Least Square (AGSA-LS) for estimation of harmonics present in time varying noisy power signals. Advanced Gravitational Search Algorithm (AGSA) is a population based algorithm which realizes the concepts of exploitation and exploration to find global optimal in search space under consideration. In AGSA, Newtonian law of gravity and laws of motion are explored to optimize mathematically the location of planets in search space. Proposed approach has been applied on test system from literature and results prove the effectiveness of technique in terms of precision and computational time. Results are further authenticated by estimating harmonics of real time current signal drawn by LED lamp. The proposed AGSA-LS delivers promising results compared to Genetic Algorithm (GA) and Particle Swarm Optimization with Passive Congregation based Least Square (PSOPC-LS).