In this paper, we propose a simple and relatively efficient heuristic method to determine job sequencing in the flow-shop considering multiple criteria such as processing time, due date and cost. The proposed method is applicable to the flow- shop where the jobs are released simultaneously and their processing sequence is predetermined and not changed until the whole jobs are processed. To develop this method, we mixed and modified some well-known multi-attribute decision heuristics such as the simple linear weighting scheme, the lexicographic rule and the 'elimination by aspect' rule. Some computer simulations were conducted to test the efficiency of the proposed method and it has been compared with the SWPT (Shortest Working Processing Time) rule and EDD (Earliest Due Date) rule. The results show that our method is as effective as the traditional ones in terms of mean flow time, tardiness, makespan, cycle time, machine utilization, etc., and proved to be much simpler and more flexible to be used in real situations.