This paper presents a theoretical analysis of a new zigzag C-axis inclined multi-layer ZnO thin-film bulk acoustic wave resonator (FBAR) as a viscosity sensor to monitor the lubrication performance of engine oil and other liquids. Free vibration and forced vibration for the FBAR loaded with liquids are analyzed. Equations necessary to calculate the sensitivity are derived. The numerical analysis shows that as the number of layers increases, the absolute sensitivity increases as well. The influences on the sensitivity of C-axis inclined angle, Q-factor, and thickness are also investigated. The results provide a foundation for further design of multi-layer FBAR viscosity sensors.