It is proposed and demonstrated that the fiber-optic Mach-Zehnder (M-Z) interferometer measures accurately the electro-optic (EO) coefficients of, not only the polymer thin film, but also the polymer waveguide. Furthermore, the tensor components, r13 and r33, of EO coefficient can be measured simultaneously. In contrast with the free space M-Z interferometer, the fiber-optic M-Z interferometer has some advantages, such as compact devices, simple experimental configuration, easy operation, and good stability. The outstanding advantage is that the second electrode need not be fabricated on the top of the polymer thin film. So, the measurement system is especially suitable to measure EO coefficients of the polymer samples on trial. In the measurement system, the interference output is fed back and controls the phase bias of the interferometer to decrease the requirement of the environmental stability and increase the measurement precision. The EO coefficient measurements of the PMMA-DR1 sample are r13=8.3 pm/V and r33=25.7 pm/V.