In electrical power dispatch problem, economic dispatch (ED) and environmental dispatch problems play a crucial part. Economic dispatch problem refers to the minimization of generation cost, where environmental dispatch problem refers to the minimization of emission of pollutants like CO2, SO2, and NOx from the power generation system. A quantum-inspired particle swarm optimization (QPSO) technique is presented in this paper to solve many-objective environmental economic dispatch (EED) problems. Emissions of CO2, SO2, and NOx are considered 3 different objectives, thus making it a 4-objective problem considering ED. Many-objective EED problems are defined by using a cubic criterion function, and a max/max price penalty factor is considered to convert all the objectives into a single objective to compare the final results with other well-known methods found in the literature like Lagrangian relaxation, particle swarm optimization, simulated annealing, and quantum-behaved bat algorithm. Quantum-inspired particle swarm optimization is implemented on a 6-unit system to solve many-objective EED problems, and at the same time, to show the effectiveness of QPSO in large systems, it is also implemented in a 26-unit power generation system for ED problem. The obtained results demonstrate and verify the effectiveness and robustness of QPSO to solve many-objective EED problems. This also shows that QPSO can effectively be implemented in such power dispatch problems.