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This paper establishes a linkage between a priority queue networks having intermediate queue with a flow shop scheduling under fuzzy environment. The queue discipline before the servers is considered on the basis of high priority while intermediate queue service is taken to be low priority. It is usually assumed that the various arrival rates, service rates and the processing time of the task (jobs) are either exact or probabilistic. However the real world is very complex and the complexity is due to inherent uncertainty. Hence the concept of fuzziness is introduced in the model. The α-cut approach and various fuzzy arithmetic operations are used in order to estimate the uncertainty associated with the input parameters. The waiting time of the item/job in a queue system can be supposed as the set up time for the first machine in scheduling process. The objective of the paper is to explore the optimal sequence of the jobs/items which minimize the mean queue length, average waiting time, total elapse time, when the jobs are processed in combine system. The heuristic algorithm is derived and the efficiency of purposed algorithm is made clear through a numerical illustration.