Scheduling is a enduring process where the existence of real time information frequently forces the review and modification of pre – established schedules. The real world is complex; complexity in the world generally arises from uncertainty. From this prospective, the concept of fuzzy environment is introduced in the theory of scheduling. This paper pertain to a specially structured n-jobs, 2-machines flow shop scheduling in which processing times are described by triangular fuzzy numbers. Further the average high rankings of fuzzy processing time are not random but bear a well defined relationship to one another. The present work is an attempt to develop a new heuristic algorithm, an alternative to the traditional algorithm as proposed by Johnson’s (1954) to find the optimal sequence to minimize the utilization time of machines and hence, their rental cost under specified rental policy.