In this paper, the fracture problem of a functionally graded piezoelectric material strip (FGPM strip) containing a crack perpendicular to the interface between the FGPM strip and a homogeneous layer under an electric load is considered. Material properties are assumed to be exponentially dependent on the distance from the interface. The superposition technique is used to solve the governing equations. The stresses induced by the electric load in the un-cracked laminate are calculated, and the obtained normal stress is used as the crack surface tractions with opposite sign to formulate the mixed boundary value problem. By using the Fourier transforms, the electro-mechanical fracture problem is reduced to a singular integral equation, which is solved numerically. The stress intensity factors of the internal crack and the edge crack are computed and presented for the various values of the nonhomogeneous and geometric parameters.