Flexible job-shop scheduling problem (FJSP), which is proved to be NP-hard, is an extension of the classical job-shop scheduling problem. In this paper, we propose a new genetic algorithm (NGA) to solve FJSP to minimize makespan. This new algorithm uses a new chromosome representation and adopts different strategies for crossover and mutation. The proposed algorithm is validated on a series of benchmark data sets and tested on data from a drug manufacturing company. Experimental results prove that the NGA is more efficient and competitive than some other existing algorithms.