This paper studies a queueing system wherein the distribution of the m-th interarrival time α_m -α_m-1(m≥1)depends on the number of customers in the system at time  α_m-1. Using the method of supplementary variables,the integral representation of the transient queue length distribution is obtained, of which the integrated term can be calculated recursively under the condition that the interarrival times and service times of the system have density functions.