The dynamic bandwidth allocation (DBA) algorithm has the greatest impact on the system performance in a 10-Gbps-capable symmetric passive optical network (XGS-PON). Most DBA algorithms perform DBA using only transmission requests sent from optical network units (ONUs) to optical line termination (OLT). In this paper, a new method to improve the performance by predicting the packet arrival rate of ONU and by using the predicted value and the transmission request of ONU at the same time in DBA is introduced. After the first dynamic bandwidth allocation with the request, the second dynamic bandwidth allocation is performed with the remaining bandwidth and predicted packet length. A new prediction method is proposed by applying the time sliding window method to the packet arrival rate prediction. In the proposed method, instead of predicting the packet arrival rate whenever one packet arrives, the packet arrival rate is predicted in unit time. The computer simulation showed that the proposed method performs better in packet mean delay than a method without packet prediction and a method using aggressive packet prediction. In addition, the length of the sliding window that optimizes the packet arrival rate prediction performance under burst traffic conditions is determined through simulation.