This paper considers the problem of scheduling a set of n jobs on m parallel machines to minimize total weighted tardiness. For the problem a genetic algorithm is proposed, in which solutions are encoded using the random key method suggested by Bean and new crossover operators are employed to increase performance of the algorithm. The algorithm is compared with the Modified Due-Date (MDD) algorithm after series of tests to find appropriate values for genetic parameters. Results of computational tests on randomly generated test problems show that the suggested algorithm performs better than the MDD algorithm and gives good solutions in a reasonable amount of computation time.