Lot-streaming is the process of splitting a job (lot) into sublots to allow the overlapping of operations between successive machines in a multi-stage production system. A new genetic algorithm (NGA) is proposed for an n-job, m-machine, lot-streaming flow shop scheduling problem with equal-size sublots in which the objective is to minimize the total stretch. The stretch of a job is the ratio of the amount of time the job spent before its completion to its processing time. NGA replaces the selection and mating operators of genetic algorithms (GAs) by marriage and pregnancy operators and incorporates the idea of inter- chromosomal dominance and individuals’ similarities. Extensive computational experiments for medium to large-scale lot-streaming flow-shop scheduling problems have been conducted to compare the performance of NGA with that of GA.