In the past decade, more and more researchers have concentrated on orbital-angular-momentum (OAM) based radio vortex wireless communications, which is expected to provide orthogonality among different OAM-modes. The uniform circular array (UCA) is considered as one promising antenna structure for OAM based radio vortex wireless communications. However, most studies regarding UCA focus on the scenario where the transmit and receive UCAs are aligned with each other. In this paper, we investigate the OAM based radio vortex wireless communications with non-coaxial UCA, i.e., the UCA transceivers are parallel but non-coaxial. We study the channel model and develop the mode-decomposition scheme to decompose the OAM-modes. Then, we discuss the impact of included angles on the channel model under non-coaxial scenario. Numerical results are presented to evaluate our developed scheme and show that the spectrum efficiency of the non-coaxial UCA transceiver in some cases is larger than that of the aligned UCA transceiver based radio vortex wireless communications.