This paper investigates the feasibility of damping multi-mode oscillations using unified power flow controller（UPFC） in a multi-machine power system. Firstly， the nonlinear dynamic model and the linearized Phillips-Heffron model of multi-terminal unified power flow controller（MUPFC） are derived， which is the extension of UPFC. Based on the characteristic of having more than one control channels， the means of superposing multi-auxiliary damping controllers on the multi-control loops of UPFC or MUPFC is proposed. By modal analysis， controllability indices are used to choose efficient control loops for weak modes respectively and auxiliary damping controllers are designed. Simulation results indicate that the multi-auxiliary damping controllers of one UPFC or MUPFC designed by the proposed method can achieve the suppression of multi-mode oscillations in power systems successfully.