The Poisson distribution assumption often arises in several industrial applications for modeling defects or non-conformities. In this work, we investigate the one-and two-sided performance of a new adaptive EWMA (Exponentially Weighted Moving Average)-type chart for monitoring Poisson count data. An appropriate discrete-state Markov chain technique is provided to compute the exact ARL (Average Run Length) properties. Moreover, comparative studies are conducted to demonstrate the higher sensitivity of the proposed chart in the detection of shifts with various magnitudes. Advices on how to select the appropriate chart parameters are provided and an illustrative numerical example is proposed.