The queueing model discussed in this paper relaxes the requirement that the service time be independent mutually and have identical distribution in GI/G/1 queue. It only requires that the retriction on service process be reduced to the degree that the service time is independent mutually.It follows that this queueing model is more rational than GI/G/1 queue in stimulating real-world systems. Under the relaxed restriction, the transient distribution of the queue length of the queueing system discussed is obtained by means of supplementary variables.