In evolutionary multi-objective optimization, achieving a balance between convergence speed and population diversity remains a challenging topic especially for many-objective optimization problems (MaOPs). To accelerate convergence toward the Pareto front and maintain a high degree of diversity for MaOPs, we propose a new many-objective dynamical evolutionary algorithm based on E-dominance and adaptive-grid strategies (EDAGEA). In EDAGEA, it incorporates the E_dominance and adaptive strategies to enhance the search ability. Instead of the Pareto dominance mechanism in the traditional dynamical evolutionary algorithm, EDAGEA employs the E-dominance strategy to improve the selective pressure and to accelerate the convergence speed. Moreover, EDAGEA incorporates the adaptive-grid strategy to promote the uniformity and diversity of the population. In the experiments, the proposed EDAGEA algorithm is tested on DTLZ series problems under 3–8 objectives with diverse characteristics and is compared with two excellent many-objective evolutionary algorithms. Experimental results demonstrate that the proposed EDAGEA algorithm exhibits competitive performance in terms of both convergence speed and diversity of population.