This paper provides an effective solution of generating OAM-carrying radio beams with all three polarizations: the linear, the left-hand circular, and the right-hand circular polarizations. Through reasonable configuration of phased antenna array using elements with three polarizations, the OAM radio waves with three polarizations for different states can be generated. The vectors of electric fields with different OAM states for all three polarizations are presented and analyzed in detail. The superposition of two coaxial OAM states is also carried out, and the general conclusion is provided.