Genetic algorithms have become increasingly important for researchers in resolving difficult problems because they can provide feasible solutions in limited time. Using genetic algorithms to solve a problem involves first defining a representation that describes the problem states. Most previous studies have adopted one-dimensional representation. Some real problems are, however, naturally suitable to two-dimensional representation. Therefore, a two-dimensional encoding representation is designed and the traditional genetic algorithm is modified to fit the representation. Particularly, appropriate two-dimensional crossover and mutation operations are proposed to generate candidate chromosomes in the next generations. A two-dimensional repairing mechanism is also developed to adjust infeasible chromosomes to feasible ones. Finally, the proposed approach is used to solve the scheduling problem of assigning aircrafts to a time table in an airline company for demonstrating the effectiveness of the proposed genetic algorithm.