In this work, a hybrid finite element formulation is presented to predict the flutter boundaries of circular cylindrical shells made of functionally graded (FG) materials. The development is based on a combination of linear Sanders thin shell theory and the classic finite element method. Material properties are temperature dependent and graded in the shell thickness direction according to a simple power law distribution in terms of volume fractions of constituents. The temperature field is assumed to be uniform over the shell surface and along the shell thickness. First-order piston theory is applied to account for supersonic aerodynamic pressure. The effects of temperature rise and shell internal pressure on the flutter boundaries of a FG circular cylindrical shell for different values of power law index are investigated. The present study shows efficient and reliable results that can be applied to aeroelastic design and analysis of shells of revolution in aerospace vehicles.