Under the demand of strategic air traffic flow management and the concept of trajectory based operations (TBO), the network-wide 4D flight trajectories planning (N4DFTP) problem has been investigated with the purpose of safely and efficiently allocating 4D trajectories (4DTs) (3D position and time) for all the flights in the whole airway network. Considering that the introduction of large-scale 4DTs inevitably increases the problem complexity, an efficient model for strategic-level conflict management is developed in this paper. Specifically, a bi-objective N4DFTP problem that aims to minimize both potential conflicts and the trajectory cost is formulated. In consideration of the large-scale, high-complexity, and multi-objective characteristics of the N4DFTP problem, a multi-objective multi-memetic algorithm (MOMMA) that incorporates an evolutionary global search framework together with three problem-specific local search operators is implemented. It is capable of rapidly and effectively allocating 4DTs via rerouting, target time controlling, and flight level changing. Additionally, to balance the ability of exploitation and exploration of the algorithm, a special hybridization scheme is adopted for the integration of local and global search. Empirical studies using real air traffic data in China with different network complexities show that the proposed MOMMA is effective to solve the N4DFTP problem. The solutions achieved are competitive for elaborate decision support under a TBO environment.