In this paper, we analyze the mean packet delay of a dynamic bandwidth allocation (DBA) scheme in an Ethernet passive optical network (EPON). We propose the interleaved polling system with a gated service discipline and a two-stage queue in order to investigate the delay performance of DBA scheme in an EPON. We assume that input packets arrive at an optical network unit (ONU) according to a Poisson process from several types of users. We use a continuous time queueing model in order to find the mean packet delay and the mean cycle time of an arbitrary packet. We obtain the closed form solution for the mean packet delay of the proposed gated polling system with a two-stage queue. We obtain another result on the mean packet delay by solving a system of linear equations derived from the moments of the queue length distribution. We give some numerical results to investigate the delay performances for the symmetric polling system with statistically identical stations. In addition, we compare numerical results on the closed form solution with numerical results on a system of linear equations.