For monitoring sequential Poisson observation, we employ the generally weighted moving average (GWMA) control chart developed by Sheu and Lin (2003) to detect the persistent shifts in process mean. This novel control chart is called the Poisson GWMA (PGWMA) chart. This chart has a better statistical performance than other control charts for monitoring Poisson observations, and is especially sensitive for detecting small process shifts. The PGWMA is a generalized charting model for which the PGWMA chart and c-chart are special cases. Additionally,its lower control limit is usually positive so that the beneficial downward shift in process mean can be detected; consequently, the quality improvement can be identified and possibly preserved.