This paper addresses minimizing Total Weighted Earliness/Tardiness(TWET) of jobs in a Flexible Job Shop (FJS) problem. The FJS problem is an extension of the classical Job Shop (JS) problem that implies each operation may be assigned to alternative available machines. So, a job may have alternative routing. The FJS problem with a TWET criterion is modeled as a mixed integer programming. The model is proven to be Np-complete. To solve the model, an algorithm, based on a Tabu Search approach (TS), is developed. The proposed algorithm employs TS to find the best routing of each job and a backward procedure to operations scheduling. Two neighboring functions are designed and their effect is investigated on the performance. The numerical experiments show the suggested algorithm efficiently solves the model in a reasonable CPU time.