The sound absorbing properties of a thin micro-perforated plate (MPP) coated with piezoelectric material with shunt damping technology is investigated. First a theoretical model is presented to predict the sound absorption coefficients of a thin plate attached with a piezoelectric patch and electrical circuits. Then the model is extended to analyze the sound absorption for a thin plate with micro perforations and piezoelectric material. Measurements are also carried out in an impedance tube and found to be in good agreements with the theoretical model. The sound absorption of the constructions can be much improved by tuning the electrical circuits.