Flexible job-shop scheduling problem (FJSP) is extension of job-shop scheduling problem which allows an operation to be performed by any machine among a set of available machines. In many FJSP, it is assumed that a lot which contains a batch of identical items is transferred from one machine to the next only when all items in the lot have completed their processing. In this paper, FJSP with overlapping in operations is handled. According to this approach, sublots are transferred from one machine to the next for processing without waiting for the entire lot to be processed at the predecessor machine. The study is carried out in two steps. In the first step, a new mathematical model is developed for the considered problem and compared to other model in the literature in terms of computational efficiency. However, it is quite difficult to achieve an optimal solution for real size problems with mathematical modelling approach because of its NP-hard structure. Thus, in the second step, a genetic algorithm is proposed to solve this problem. An effective chromosome representation is used and in generation of initial population, a new search methodology is developed. At the same time, efficient decoding methodology is adopted considering only active schedule in order to reduce the search space. The proposed algorithm was tested on benchmark problems taken from literature of different scales. Obtained results were compared with the results obtained by other algorithms. Computational studies show that our algorithm surpasses other known algorithms for the same problem, and gives results comparable with the best algorithm known so far.