Increasing optimizing criteria in modern power systems promotes the birth of many-objective optimal power flow (Ma-OPF) problems in which more than three optimizing objective functions are considered. The increasing optimizing objectives as well as complex constraints of power balance and other system limits bring a decrease in selection pressure and challenges of constraint handling techniques for traditional multi-objective evaluation algorithms. Aiming at the solving difficulties of Ma-OPF problems, an improved NSGA-III integrating eliminating strategy and dynamic constraint relaxation mechanism (NSGA-III-EDR) is proposed. In the proposed approach, a new elimination strategy that eliminates the associated points having the largest angle with the corresponding reference line is employed to increase the selection pressure of the algorithm. An integrated constraint handling method, which employs a repair strategy based on assigning decision variables to feasible values and a penalty function approach together to handle power flow equality constraints, is also introduced into the NSGA-III-EDR. Aiming at lacking feasible solutions of the algorithm in the early searching stage, a strategy of relaxing constraint violations as well as a dynamic updating strategy for the tolerated threshold value of distinguishing feasible and infeasible solutions at the early evolution is proposed. Moreover, an improved domination sorting rule based on the proposed constraint handling method and the relaxing strategy to constraint violations is employed to promote the generation of feasible solutions. The effectiveness and feasibility of the proposed improved NSGA-III-EDR approach are studied and evaluated on different test cases of a famous standard IEEE 30-bus power system as well as the larger power systems of IEEE 57-bus and IEEE 118-bus. The numerical results show that the proposed NSGA-III-EDR method can provide solutions to many-objective OPF problems with tremendous potential compared with the traditional NSGA-III and other algorithms illustrated in the literature.