According to the structure feature of the governing equations of space axisymmetric problem in transversely, isotropic piezoelectric material. using the method of introducing potential function one by one, in this paper we obtain the so-called general solution of displacement and eleclric potential function denoied by unique poiential function which satisfies specific partiality equations. As an applying example of the general solution, we solve problem of semi-infinile body made of piezoelectric material, on the surface of the semi-infinite body a concentrative force is applied, andget the analytic formulations of stress and electric displacement comiponenis. The general solution provided by this paper can be used as a tool to analyse the mechanical-electrical coupling behavior of piezoelecrtic material which conlains defects such ascavity, inclusion, penny-shape crack, and so on. The result of the solved problem canbe used directly to analyse contact problems which take place between two piezoelectric bodies or piezoelectric body and elastic body.